a car accelerates uniformly from rest and acquires a speed of 36 km/hr in 10 seconds. Find the total distance travelled in metres.
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Given :
- initial velocity of Car , u = 0
- final velocity of Car , v = 36 km h⁻¹
final velocity of Car , v = 36×5/18 = 10 ms⁻¹
- time taken for changing velocity , t = 10 s
To find :
- total distance travelled by Car to reach the velocity of 36 km/h
Formula used :
- First equation of motion
v = u + a t
- second equation of motion
s = u t + 1/2 a t²
( where v is the position of image , u is the position of object , a is the acceleration , t is the time taken , s is the distance traveled )
Solution :
Let , acceleration of car be a
then,
using first equation of motion
→ v = u + a t
→ 10 = 0 + a ( 10 )
→ a = 10 / 10
→ a = 1 ms⁻²
Now ,
using second equation of motion
→ s = u t + 1/2 a t²
→ s = (0) (10) + 1/2 (1) (10)²
→ s = 0 + 1/2 (100)
→ s = 50 m
Therefore,
Distance traveled by Car will be 50 metres.
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