Question

The variation of speed (in m/s) of an object with time (in seconds) is given by the expression $V(t) = V_0 - 5t + 5t^2$

• A. At time t = 0 s, the instantaneous acceleration is zero
• B. At time t = 0 s, there is a deceleration of the object
• C. At time t - 1 s, the object is at rest
• D. At time t = 1 s, the instantaneous acceleration is zero

Answer 1

Answer: (B)

At time t = 0 s, there is a deceleration of the object

Answer 2

The velocity of a object is given by equation
$v(t)=v_{0}-5 t+5 t^{2}$
Acceleration
$a=\frac{d v}{d t}=\frac{d}{d t}\left(v_{0}-5 t+5 t^{2}\right)=-5+10\, t$
at $t=0$ the acceleration of object
$a=-5+10(0)=-5\,ms ^{-2}$
So, at time $t=0$, there is deceleration of object.
at $t=1\, s,\, v=v_{0}-5+5=v_{0} ms ^{-1}$
and $a=-5+10=+5\,ms ^{-2}$
So, at $t=0$, there is non zero and positive value of velocity and acceleration.