A particle starts moving rectilinearly at time t = 0 such that its velocity ‘v’ changes with time ‘t’ according to the equation v=t2−t where t is in seconds and v in m/s. Find the time interval for which the particle retards.
t = 0.5 s to t = 1 s
Velocity, v=t2−t
Acceleration, a=dvdt=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.