Question

Acar of mass 1 metric ton starts from rest and accelerates to a speed of 72 km/h in 20 seconds. It

then moves with a constant velocity for 80 seconds, and is brought to rest in next 10 second.

1.
what is the total distance traveled by the car?​

Answer 1

Answer:

1900m

Explanation:

Since car starts from rest therefore:

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Initial velocity = u = 0m/s

The car accelerates to 72km/h

$= 72 \times 5 \div 18$

$= 20ms$

Final velocity = 20m/s = v

It reaches 20m/s in 20seconds

Therefore, T = 20s.

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For a body in motion acceleration :

= Final velocity - Initial velocity

Time

After inputting the values in formula we get =>

Acc = 20 - 0

20

Acc = 20/20

$acc = 1m \div {s}^{2}$

Therefore acceleration of the car is 1m/s^2.

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Now according to third equation of motion =>

The square of final velocity of a body is equal to sum of square of its initial velocity and double of product of acceleration and distance or displacement.

${v}^{2} = {u}^{2} + 2as$

After inputting upper values in this we get =>

${20}^{2} = {0}^{2} + 2(1)(s)$

${20}^{2} = 2s$

After shifting (2) to R. H. S :

$s = 400 \div 2$

s = 200m.

Therefore the distance covered by car in first time is 200m .

200m--------------(s1)

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Now it is given that the car then moves with same velocity till 80seconds.

Thus in this case

Initial velocity = u = 20m/s

Time for which it travels = 80 seconds

Therefore the distance it travels again = Speed × Time

= 80 × 20

= 1600m. ----------------(s2)

After covering this much distance the car comes to rest in 10 seconds.

Since car comes to rest in this case

v= 0m/s

Now acceleration i.e. (Retardation here)

will be =>>

$0 - 20 \div 10$

= -2m/s^2

(-) shows opposite direction

According to third equation of motion

${v}^{2} = {u}^{2} + 2as$

After inputting values in this we get:

$0 = {20}^{2} + 2( - 2)s$

${ - 20}^{2} = - 4s$

${20}^{2} = 4s$

After shifting (4) to L. H. S :

$400 \div 4 = s$

s = 100m --------------------(s3)

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On adding s1, s2 and s3 wr get

200m + 1600m + 100m

= 1900m

Therefore total distance covered by car is 1900m.

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BY SCIVIBHANSHU

THANK YOU

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