The only force acting on a 2.5 kg body as it moves along the positive x axis has an x component Fx = -7x N, where x is in meters. The velocity of the body at x = 2.6 m is 8.5 m/s.

(a) What is the velocity of the body at x = 3.3 m?
(b) At what positive value of x will the body have a velocity of 2.8 m/s?

v = 5.69 m/s

x = 4.43 m

Explanation:

Mass of the body m = 2.5 kg

force acting on the body = - 7 x N

From the Newton's second Law;

; Then:

Integrating on both sides ; we have :

where; k is the integral constant ;

At x = 2.6 m speed is 8.5 m/s

Then;

However:

a)

At x = 3.3 m; speed of the object

b)

speed of the body is 2.8 m/s; then

what was the acceleration of the 2 kg cart?

⇒ 16.0 cm/s2

what was the acceleration of the 4 kg cart?

⇒ 8.1 cm/s2

what was the acceleration of the 6 kg cart?

⇒ 5.3 cm/s2