The acceleration of a cart started at t=0 varies with time as shown in figure. Find the distance traveled in 30 second and draw the position time graph.
Answers
Answer: Total Distance Travelled in 30sec = 1000 ft.
Explanation: In 1st 10 sec S1 = ut + 1/2 at^2
= 0 + 1/2 × 5 × 10^2
= 250 ft.
At 10 sec v = u + at
= 0 + 5 × 10
= 50 ft/sec
From 10 to 20 sec (Δt = 20 - 10 = 10sec) it moves with uniform velocity 50 ft/sec, distance S2 = 50 × 10
= 500 ft.
Between 20 sec to 30 sec acceleration is constant i.e. -5 ft/s^2. At 20 sec velocity is 50 ft/sec.
t = 30 - 20
= 10s
S3 = ut + 1/2 at^2
= 50 × 10 + 1/2 (-5) (10)^2
= 250 m.
Total distance travelled in 30 sec = S1 + S2 + S3
= 250 + 500 + 250
= 1000 ft.
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