Question

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?
please don't answer if don't know

Answer 1

Answer :-

(a) Total distance travelled is 120 m .

(b) Speed at the 8th second is 54 km/h .

(c) (i) 1.67 m/s²

(ii) 0 m/s²

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Firstly, let's calculate the acceleration of the car (from 0-6 seconds ).

v = u + at

⇒ 15 = 5 + 6a

⇒ a = 1.67 m/s²

For number (a) :-

From the graph, we can understand that the car moves with uniform acceleration from 0-6 sec and with constant velocity from 6-10 sec .

Distance travelled from 0-6 seconds :-

s = ut + ½at²

⇒ s = 5(6) + ½ × 1.67 × 36

⇒ s = 30 + 30

⇒ s = 60 m

Distance travelled from 6-10 seconds :-

= Speed × Time

= 15 × 4

= 60 m

Total distance :-

= (60 + 60) m

= 120 m .

For number (b) :-

At the 8th second, the car is moving with a velocity of 15 m/s.

Speed in km/h :-

= 15 × 18/5

= 54 km/h

For number (c) :-

(i) We have calculated at first only that acceleration of the car during first 6 seconds is 1.67 m/s² .

(ii) During the last 2 seconds, the car is moving with a constant velocity of 15 m/s, so it's acceleration is 0 m/s² .

Answer 2

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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

1. (i) During the first 6 s
2. (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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