Question

Multiple Correct Answers Type:
A particle moves along a straight line and its velocity depends on time as v = 4t - $t^2$. Then for first 5 s:

• A. Average velocity is 25/3 m/s
• B. Average speed is 10 m/s
• C. Average velocity is 5/3 m/s
• D. Acceleration is 4 $m{s}^{-2}$ at t=0

Answer 1

Answer: (C), (D)

The correct options are
C Average velocity is 5/3 m/s
D Acceleration is 4 $m{s}^{-2}$ at t=0

For, 1st second $v_1=4-1=3m/s$

For, 2nd second $v_2=8-4=4m/s$

For, 3rd second, $v_3=12-9=3m/s$

For, 4th second, $v_4=16-16=0m/s$

For, 5th second, $v_5=20-25=-5m/s$

Therefore, $v_{avg}=\frac{v_1+v_2+v_3+v_4+v_5}{3}$

or, $v_{avg}=\frac{5}{3}m/s$.

Option (C) is therfore correct.

Acceleration is the rate of change of velocity with respect to time.
$\frac{dv}{dt}=a$

or, $a=4-2t$

Using $t=0$, we get, $a=4m/s^2$.

Option (D) is also correct.