Question

A particle starts moving rectilinearly at time t = 0 such that its velocity ‘v’ changes with time ‘t’ according to the equation $v=t^2-t$ where t is in seconds and v in m/s. Find the time interval for which the particle retards.

• A. t = 0 to t = 1 s
• B. t = 0.5 s to t = 1 s
• C. t = 0 to t = 0.5 s
• D. t > 1 s

Answer 1

The correct option is B

t = 0.5 s to t = 1 s

Velocity, $v=t^2-t$
Acceleration, $a=\frac{dv}{dt}=2t-1$
The particle retards when acceleration is opposite to velocity.
Now, v is positive when t > 1 s and negative when t < 1 s.
Similarly, a is positive when t > 0.5 s and negative when t < 0.5 s.
So, for the interval t = 0.5 s to t = 1 s, velocity and acceleration have opposite signs and the particle is retarding.