Test: Instantaneous Velocity and Speed - ACT MCQ

At time = 10s, the distance covered is 5m. Velocity = distance/time. Hence, velocity v at 10s = 5/10 = 0.5 m/s.

This type of motion can be called circular motion with increasing radius. As the radius increases, the tangential velocity increases (v = rw). Now, as there is only one velocity present, the speed will be equal to the magnitude of the tangential velocity.

The function for velocity can be derived by differentiating the equation with respect to t. v = 2(t - 4) is the required function. When t = 5, v = 2(5 - 4) = 2.

Instantaneous velocity describes the velocity of an object at a given time instant. Average speed is the speed at which the object travels throughout the time period and not an instant. Speed is a scalar quantity; hence it cannot show the direction of motion.

The instantaneous velocity will increase with time. If the motion is accelerated, no matter if the acceleration is constant, or variable, the instantaneous velocity will increase. Variation of acceleration describes how to change in velocity is changing.

When the ball rises up, there will be a point where it will be in the state of instantaneous rest. At the this position the speed of the ball will be 0. Speed is maximum at the initial and final points.

The correct formula is v = dx/dt. Instantaneous velocity is the velocity of the object at a given time instant. v = x/t is the formula for average velocity.

Given:

Acceleration is uniform.

S₁₁ = 640 cm 

S₁₅ = 840 cm

Formula:

Distance traveled in nth second  

where u is the initial velocity and a is the acceleration.

Calculations:

S11 = u + a/2(2 × 11 - 1)

⇒ 640 = u + 21a/2   ---   (i)

S15 = u + a/2(2 × 15 - 1)

⇒ 840 = u + 29a/2   ---  (ii)

Subtracting (i) from (ii) :

⇒ 200 = 4a

⇒ a = 50 cm/s²

Putting a = 50 in (i) -

u = 115 cm/s

Concept

• Uniform Linear motion: The motion of an object in which the object travels in a straight line and its velocity remains constant along that line as it covers equal distances in equal intervals of time, irrespective of the duration of the time.
  • Example: Ball moving on a frictionless surface with constant velocity.
  • In this type of motion, the net force on the body will be zero.
• Non-uniform motion: The motion of an object in which the object travels with varied speed and it does not cover the same distance in equal time intervals, irrespective of the time interval duration.
  • Example: The motion of a train
  • There is some net force acting on the body in non-uniform motion.
  • It is also called the accelerated motion.

Explanation

• In the case of the uniform linear motion, there is no change in the velocity of the body. So the net force on the body will be zero.
• Hence option 1 is correct.
• In the case of circular motion, there will be a centripetal force always acting on the body even if it is a uniform circular motion. 

Concept:

Velocity: The displacement per unit time is called velocity.

where v is the velocity, Δx is the change in displacement, Δt is the change in time.

A body comes to rest when the velocity is zero.

Calculation:
Given that position of a particle is given by: x = -2t² + 4t

A body comes to rest when the velocity is zero.

v = −4t + 4 = 0

t = 1 sec