A 10 kg space probe travels in a straight line with initial velocity 20 m/s. The

Question

A 10 kg space probe travels in a straight line with initial velocity 20 m/s. The engines apply a force F=5t in the direction of motion, where F is in Newtons and t is in seconds. If the engines run for 10 seconds,

a)      What is the final velocity of the probe?

b)       What distance did it travel while the engines were on?

A 10 kg space probe travels in a straight line with initial velocity 20 m/s. The engines apply a force F=5t in the direction of motion, where F is in Newtons and t is in seconds. If the engines run for 10 seconds, What is the final velocity of the probe? What distance did it travel while the engines were on?

Explanation / Answer

a) acceleraion = force / mass = 5t / 10 = 0.5 * t

so.. dv / dt = 0.5 t

so.. v_final - v_initial = (0.5/2) * ( t_final^2 - t_initial^2 )

so.. v_final - 20 = 0.25 * ( 100 - 0 )

so.. v_final = 45 m/sec

b) so.. v(t) = 20 + 0.25 t^2

so.. dx / dt = 20 + 0.25 t^2

so.. x = 20t + (0.25/3) t^3

so.. for t = 10 secs ..

distance x = 283.333 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.