Question

A 5 kg particle moving along the x-axis experiences the Net Force F_x = 10t, where t is in seconds. The particle has a velocity of 2 m/s at t = 1s. Find the particle's velocity at t = 5s:

a. 24 m/s

b. 26 m/s

c. 27 m/s

d. 25 m/s

Answer 1

Explanations & calculations

• Since the force is a variant of time the acceleration also follows.
• Therefore,

$\qquad\qquad \begin{aligned} \small F&=\small ma=m\frac{dv}{dt}\\ \small dv&=\small \frac{F}{m}.dt=2t.dt\\ \small \int_1^5 dv&=\small 2\int_1^5t.dt\\ \small v\Big|_1^5&=\small t^2\Big|_1^5\\ \small V_5-2&=\small 25-1\\ \small V_5&=\small 26\,ms^{-1} \end{aligned}$