The velocity−time graph for the motion of a car is shown in the given figure.
(a) What is the total distance travelled by the car?
(b) What is the speed of the car (in km/h) at 8th second?
(c) What is the acceleration of the car
(i) during the first 6 s?
(ii) during the last 2 s?
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Answers
Answer:
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To Find
(a) What is the total distance travelled by the car?
(b) What is the speed of the car (in km/h) at 8th second?
(c) What is the acceleration of the car
(i) During the first 6 s
(ii) During the last 2 s
Solution
Calculating acceleration of car from 0-6 s,
➝ v = u + at
➝ 15 = 5 + 6a
➝ 15 - 5 = 6a
➝ 6a = 10
➝ a = 10/6
After cancelling, we get :-
➝ a = 1.67 m/s²
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◈ (a)Calculating distance travelled in 0-6 s,
➳ s = ut + 1/2 at²
➳ s = 5 × 6 + 1/2 × 1.67 × 36
➳ s = 30 + 30
➳ s = 60 m
Calculating distance travelled in 6-10 s,
➪ Distance = Speed × Time
➪ Distance = 15 × 4
➪ Distance = 60 m
So, total distance :-
⪼ 60 + 60
⪼ 120 m
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◈ (b)At 8th s, car us moving with velocity 15 m/s
So,
→ Speed in km/h = 15 × 18/5\:
→ Speed in km/h = 54 km/h
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◈ (c)Acceleration of car during 1st 6s is calculated above, i.e, 1.67 m/s²
During last 2 s, car us moving with constant velocity of 15 m/s. So, it's acceleration is 0 m/s²
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