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The basic difference between a scalar and vector is one of
Scalar quantity gives you an idea about how much of an object there is, but vector quantity gives you an indication of how much of an object there is and that also in which direction. So, the main difference between these two quantities is associated with the direction, i.e. scalars do not have direction but vectors do.
Explanation:An object that falls through a vacuum is subjected to only one external force, the gravitational force, expressed as the weight of the object. An object that is moving only because of the action of gravity is said to be free falling and its motion is described by Newton's second law of motion. With algebra we can solve for the acceleration of a free falling object. The acceleration is constant and equal to the gravitational acceleration g which is 9.8 meters per square second at sea level on the Earth. The weight, size, and shape of the object are not a factor in describing a free fall.
Explanation:The net acceleration of a particle in circular motion is along the radius of the circle towards the centre Only in case of uniform circular motion.
When a ball is thrown upwards, as it rises, the vertical component of its velocity
Explanation:if a ball is thrown upward at an angle? The ball has a vertical and a horizontal component of velocity. The force of gravity is acting on it and its acceleration is in the downward direction. The vertical component of velocity is therefore changing. As the motion and acceleration is in opposite direction so vertical component of velocity decrease.
Explanation:Parallelogram law of vector addition is,If two vectors are considered to be the adjacent sides of a Parallelogram, then the resultant of two vectors is given by the vector which is a diagonal passing through the point of contact of two vectors.
Explanation:The sum of two or more vectors is called the resultant. The resultant of two vectors can be found using either the triangle method or the parallelogram method.
Explanation:A particle with a vertical and horizontal velocity travelling in a gravitational field will trace out a parabola.
The reason why cyclists bank when taking a sharp turn is
Explanation:In order to take a safe turn, the cyclist has to bend a little from his vertical position. In this case, a component of the reaction provides the required centripetal force.If q is angle made by the cyclist with the vertical then
In actual practice, the value of q is slightly less because the force of friction also contributes towards the centripetal force.
Explanation:The maximum possible value for displacement is the distance travelled, so it cannot be of a greater value than distance (path length).The magnitude of the displacement is always less than or equal to the distance traveled. If two displacements in the same direction are added, then the magnitude of their sum will be equal to the distance traveled.
Explanation:Vector addition is the operation of adding two or more vectors together into a vector sum. The socalled parallelogram law gives the rule for vector addition of two or more vectors. For two vectors, the vector sum is obtained by placing them head to tail and drawing the vector from the free tail to the free head.
A motorcycle stunt rider rides off the edge of a cliff. Just at the edge his velocity is horizontal, with magnitude 9.0 m/s. Find the magnitude of the motorcycle’s position vector after 0.50s it leaves the edge of the cliff.
Explanation:The motorcycle’s x and ycoordinates at t=0.50 s are
The negative value of y shows that the motorcycle is below its starting point.
The motorcycle’s distance from the origin at t=0.50 s is
Explanation:Equal vectors are vectors that have the same magnitude and the same direction. Equal vectors may start at different positions.
Explanation:Angular momentum is a vector quantity (more precisely, a pseudovector) that represents the product of a body's rotational inertia and rotational velocity about a particular axis.
A sports car has a “lateral acceleration” of 0.96g = 9.4 m ^{s−2}. This is the maximum centripetal acceleration the car can sustain without skidding out of a curved path. If the car is traveling at a constant 40 m/s on level ground, what is the radius R of the tightest unbanked curve it can negotiate?
Explanation:
The car is in uniform circular motion because it’s moving at a constant speed along a curve that is a segment of a circle. Hence we know
This is the minimum turning radius because arad is the maximum centripetal acceleration.
A cyclist moves along a circular path of radius 70m. If he completes one round in 11s, calculate total length of path.
Radius of the circular path, r = 70m
Time takes to complete one round, t = 11s
Total length of the path, s = 2πr = 2*22/7*70 = 440m
Work is the energy transferred to an object by force. It is a scalar quantity because it's the product of force and displacement. Work is not the same thing as force, which is a vector quantity, because work is the result of force.
In a harbor, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbor flutters along the NE direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?
Explanation:The flag is fluttering in the northeast direction. It shows that the wind is blowing toward the northeast direction. When the ship begins sailing toward the north, the flag will move along the direction of the relative velocity (vwb) of the wind with respect to the boat.
Hence, the flag will flutter approximately due east.
Explanation:Vector addition is commutative, just like addition of real numbers. If you start from a point say P, you end up at the same spot no matter which displacement (a or b) you take first. The headtotail rule yields vector c for both a + b and b + a.
Which of the following algebraic operations on vectors not permissible?
Explanation:Although vectors and scalars represent different types of physical quantities, it is sometimes necessary for them to interact. While adding a scalar to a vector is impossible because of their different dimensions in space, it is possible to multiply a vector by a scalar.
A man can swim with a speed of 4.0 km/h in still water. How long does he take to cross a river 1.0 km wide if the river flows steadily at 3.0 km/h and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?
Explanation:
Speed of the man, v_{m} = 4 km/h
Width of the river = 1 km
The addition of vectors and the multiplication of a vector by a scalar together gives rise to
Explanation:
If a vector is multiplied by a scalar as in pA^{→} , then the magnitude of the resulting vector is equal to the product of p and the magnitude of A^{→}, and its direction is the same as A^{→} if p is positive and opposite to A^{→} if p is negative.
Distributive law for scalar multiplication:
p(A^{→} +B^{→} )=pA^{→} +pB^{→}
Explanation:A displacement is vector that is the shortest path length from the initial to the final position of the body. It is not always eqaul to path length. It can be zero and ve also.
Rain is falling vertically with a speed of 30 m ^{s−1}. A woman rides a bicycle with a speed of 10 m s^{−1} in the north to south direction. What is the direction in which she should hold her umbrella?
The described situation is shown in the given figure.
Here,
v_{c} = Velocity of the cyclist
v_{r} = Velocity of falling rain
In order to protect herself from the rain, the woman must hold her umbrella in the direction of the relative velocity (v) of the rain with respect to the woman.
Hence, the woman must hold the umbrella toward the south, at an angle of nearly 18° with the vertical.
Explanation:A null vector is a vector having magnitude equal to zero.It is represented by 0^{→}.A null vector has no direction or it may have any direction.Generally a null vector is either equal to resultant of two equal vectors acting in opposite directions or multiple vectors in different directions.
0^{→} =A^{→} +(−A^{→} )
A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity?
(b) Distance between the hostel and the station = 10 km = Displacement of the car
∴ Average velocity =
A projectile is fired a velocity of 150 meters per second at an angle of 30 degrees with the horizontal. What is the magnitude of the vertical component of the velocity at the time the projectile is fired?
Explanation:
Initial velocity u = 150 m/s
Explanation:Acceleration is a vector quantity because it has both magnitude and direction.When an object has a positive acceleration, the acceleration occurs in the same direction as the movement of the object.When an object has a negative acceleration (it's slowing down), the acceleration occurs in the opposite direction as the movement of the object.
We can define the difference of two vectors A and B as the
Explanation:
Vector subtraction is defined in the following way.
Thus vector subtraction can be represented as a vector addition.
Three girls skating on a circular ice ground of radius 200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in Figure. What is the magnitude of the displacement vector for each ? For which girl is this equal to the actual length of path skate ?
Explanation:
(i) PQ = diameter = displacement for each girl = 2r = 2 x 200 = 400 m
Since, displacement vector does not depend upon the actual path length and it is the shortest distance between initial and final position, so in the case of each girl the displacement is 400 m.
(ii)This is equal to the actual length of the path skated by girl B.
Explanation:Electric current is a scalar quantity.It represents the direction of flow of positive charge but it is treated as a scalar quantity because current follows the laws of scalar addition and not the laws of vector addition,because the angle between the wires carrying current does not effect the total current in the circuit.
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