# What is the acceleration of a car that can reach a speed of 360 km/h from rest within 24 seconds. What is the distance traveled by the car in this duration of time?

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### 1 Answer

If the initial velocity of a car is u and it accelerates at a rate a for time t, the final velocity is v is equal to v = u + a*t. The distance traveled by the car in reaching the speed v is equal to `(v^2 - u^2)/(2*a)` .

Here, the initial speed of the car is 0 km/s = 0 m/s as it is at rest. The speed of the car after 24 seconds is 360 km/h = 100 m/s. Using the formulas given earlier, the acceleration of the car in the 24 seconds taken to reach a speed of 100 m/s is `(100 - 0)/24 = 25/6 ~~ 4.167` m/s^2

The distance traveled by the car in this duration of time is equal to `(100^2 - 0^2)/(2*(25/6)) = (100^2*6)/50`

=> 1200 m

The average acceleration of the car over 24 seconds is 4.167 m/s^2 and it travels 1200 m.