Question

Solve this:
Q.16. The acceleration of a cart started at t = 0, varies with time as shown in figure. Find the distance travelled in 30 seconds and draw the position-time graph.

Answer 1

Hello dear,
First of all you didn't give question graph. I'll post that.

● Answer -
s = 1000 ft = 300 m

● Explanation -
For first 10 s, a = 5 ft/s^2
s1 = ut + 1/2 at^2
s1 = 0×10 + 1/2 × 5×10^2
s1 = 250 ft

For next 10 s, a = 0
s2 = vt
s2 = 50 × 10
s2 = 500 ft

For next 10 s, a = -5 ft/s^2
s3 = ut + 1/2 at^2
s3 = 50×10 + 1/2 (-5)×10^2
s3 = 250 ft

Total distance traveled in 30 s,
s = s1 + s2 + s3
s = 250 + 500 + 250
s = 1000 ft
s = 300 m

Hence, total distance travelled is 1000 ft i.e. 300 m.

[Position-time graph is attached as image.]

Hope this helped you...