Question

The acceleration $a$ of particle varies with time $t$ as shown. Find an expression for velocity in terms of $t$. Given velocity is zero at $t=0$.

• A. $v=t^2+2t$
• B. $v=t^2-2t$
• C. $v=2t^2-2t$
• D. $v=t^2+4t$

Answer 1

Answer: (B)

$v=t^2-2t$

$y=mx+c$

$a=mt+c$

For $t=1$ $0=m+c$

For $t=0$ $-2=0+c$

$c=-2$

$a=2t-2$

$\frac{dv}{dt}=2t-2$

$dv=(2t-2)dt$

$v{|}_0^v=t^2-2t{|}_0^t=t^2-2t-(0{)}^2+2(0)=t^2-2t$