Question

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 is in m/s. Find the time interval for which the particle retards.

• A. (1)/(2)
• B. (1)/(2)>t>1
• C. (1)/(4)
• D. (1)/(2)

Hint:

Retardation means acceleration opposite to velocity.

Answer 1

The Correct Option is A

Step 1: Acceleration,
a = (dv)/(dt) = 2t - 1 

Step 2: Retardation occurs when velocity and acceleration have opposite signs. 

Step 3: Solving gives,
1/2 < t < 1