Test: Motion in a Plane with Constant Acceleration - ACT MCQ

From the given options, the only motion that can possibly have a uniformly accelerated motion in a plane is that of a particle. In circular motion the direction of the acceleration keeps changing and in a pendulum and in a spring, both the magnitude and directions keep changing.

The distance between A and B is 13 units. The distance between B and C is 10 units. Hence, the total distance is 23 units. The total time taken is 20 s. Average speed = total distance/total time taken = 23/20 = 1.15 units/s.

The initial position of the car is at the origin and the final position is 25î – 75ĵ. Hence the displacement is 25î – 75ĵ. The total time taken is 25 s. Hence, the velocity = change in position/time = î – 3ĵ.

The acceleration of a body is the rate at which the velocity changes with time. Here, the change in velocity is 7ĵ. The total time taken is 10s. Hence, the acceleration = change in velocity/time = 0.7ĵ.

The body’s displacement is given by s = (1/2)at². The body starts from the origin hence, the total displacement is the final position of the body. Therefore, after putting in the values, we get, s = (1/2)(11î + 7ĵ)*10² = 550î + 350ĵ.

The distance between A and B is 10 units. The distance between B and C is 5 units. Hence, the total distance is 15 units. The total time taken is 100 s. Average speed = total distance/total time taken = 15/100 = 0.15 units/s.

The velocity of a body is the rate at which the displacement changes with time. Here, the change in position is the change in displacement, and is 14î + 11ĵ. The total time taken is 20s. Hence, the acceleration = change in displacement/time = 0.7î + 0.55ĵ.

Angular velocity is the time rate at which an object rotates, or revolves, about an axis, or at which the angular displacement between two bodies changes. Thus the rate of change of angular velocity depends on angular displacement.

Let the point 4m from east of P be A. So PA is 4m and the point in the north be B such that AB is 3m. Therefore PBA is a right-angled triangle. The resultant displacement is equal to PB
PA² + AB² = PB²
4² + 3² = PB²
16 + 9 = 25 = PB²
PB = 5m

The path that an object with mass in motion follows through space as a function of time is called a trajectory or flight path. The total distance between the source and the target position is called the slant range. The angle formed between them is called the Inclination Angle.