Question Type 1: Given the displacement or velocity, finding the velocity or acceleration respectively Exercises

Given the velocity $v(t)=t \, e^{-2t}$, find the acceleration $a(t)$.

Given the displacement $s(t)=\frac{\sin t}{t}$, find the velocity $v(t)$.

Given the velocity $v(t)=6t^2-4t+3$, find the acceleration $a(t)$.

Given the velocity $v(t)=\frac{e^t}{t}$, find the acceleration $a(t)$.

Given the displacement $s(t)=4t^3-2t^2+t-7$, find the acceleration $a(t)$.

Given the displacement $s(t)=\sin(t^2)$, find the acceleration $a(t)$.

Given the displacement $s(t)=t^3\sin t$, find the velocity $v(t)$.

Given the displacement $s(t)=5t^2-3t+2$, find the velocity $v(t)$.

Given the displacement $s(t)=e^{2t}$, find the velocity $v(t)$.

Given the displacement $s(t)=e^{-t}+\sin(2t)$, find the velocity $v(t)$.

Given the velocity $v(t)=\ln(\sin t)$, find the acceleration $a(t)$.

Given the velocity $v(t)=\ln(t^2+1)$, find the acceleration $a(t)$.