Test: Acceleration - ACT MCQ

Acceleration = dv/dt = d²x/dt². The velocity (v) can be expressed as, v = dx/dt = 5cos(5t). Hence acceleration (a) becomes, a = dv/dt = -25sin(5t).

Acceleration of a body can be found out by differentiating the expression for velocity. Here v = 5t³. On differentiating, a = dv/dt = 15t². On putting t = 2, we get a = 60 units.

Acceleration is the rate of change of velocity. Here, the velocity changes form 3 m/s to 5 m/s in 5s. Hence, acceleration = (5-3)/5 = 0.4 m/s².

Deceleration always acts in the direction opposite to the direction of motion. Magnitude of deceleration is 60 m/s² and it acts in the direction opposite to North. Hence the answer is 60 m/s² Southwards.

Assuming the ball falls with zero initial velocity, then according to the second equation of motion, s = ut + (1/2)at² = (1/2)at². When we put t = 10s, we get a = 0.1 m/s².

Here we use the second equation of motion. s = ut + (1/2)at². In a uniformly accelerated motion, the acceleration remains constant. Therefore, the equation for displacement becomes the equation of a parabola.

Velocity varies parabolically implies that velocity is of the form at + bt². On differentiating the velocity, we get the equation for acceleration. Therefore, a = dv/dt = a+2bt, which is a linear equation. Hence the acceleration varies linearly.

The gradient or slope of any graph tells us the value of its differential at that point. Since acceleration is the differential of velocity with respect to time, the gradient is equal to the acceleration.

Since the body is accelerated, the speed and velocity will vary. Momentum depends on velocity; hence the momentum will also vary. The force remains constant as F = ma.

Negative acceleration is known is deceleration. Negative acceleration acts in the direction opposite to the direction of motion. It is also known as retardation.