Question

a 5 kg moves under the influence of aforce F=(4t²i-4tj)N,where t is the time of second.it start from the origin at t=0.find its velocity

Answer 1

mass of particle , m = 5kg

force is given as, F = (4t²) i - (4t) j , where t is the time of second.

we know, from Newton's 2nd law of motion.

F = ma

so acceleration, a = {(4t²)i - (4t) j}/5

= (0.8t²)i - (0.8t) j

we know, acceleration is the rate of change of velocity with respect to time.

i.e., dv/dt = a = (0.8t²)i - (0.8t) j

or, ∫dv =[ ∫(0.8t²)dt ]i - [∫(0.8t)dt ]j

or, v - v0= 0.8t³/3 - 0.4t²

[ let v0 is the velocity at t = 0.]

so, v = 0.8t³/3 - 0.4t² + v0

hence, velocity after time t = 0.8t³/3 - 0.4t² + v0