Question

Velocity of a particle varies with time as v=4t. The displacement of particle between t=2 to t=4 sec, is:-

• A. 12 m
• B. 36 m
• C. 24 m
• D. 6 m

Answer 1

Answer: (C)

24 m

We know that velocity is $\frac{dx}{dt}=v=4t$ so $dx=4tdt$

integrating both sides we get ${\int }_{x_1}^{x_2}dx={\int }_{t=2}^{t=4}4tdt$

or displacement $=x_2-x_1=2t^2{|}_2^4=2(16-4)=24m$