A CAR TRAVEL WITH A VELOCITY OF 18km PER HOUR.IT THEN ACCELERATE UNIFORMLY AND TRAVEL A DISTANCE AT 50m, IF THE VELOCITY REACHES IT 54km 1HR,FIND THE ACCELERATION AND THE TIME TO TRAVEL THIS DISTANCE.
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A car travelling at 36km/h it then accelerates uniformly and travel a distance of 50m if the velocity reached is 54km/h find the accelaration and the time to travel this distance
To find the acceleration and time it took for the car to travel a distance, we can use the equations of motion.
Let's break down the information given:
Initial velocity (u) = 18 km/h = 5 m/s (converted by multiplying by 1000/3600)
Final velocity (v) = 54 km/h = 15 m/s (converted by multiplying by 1000/3600)
Distance (s) = 50 m
We need to find:
Acceleration (a)
Time (t)
We can use the following formula to find acceleration when initial velocity, final velocity, and distance are given:
v² = u² + 2as
Rearranging the formula to solve for acceleration:
a = (v² - u²) / (2s)
Substituting the given values:
a = (15² - 5²) / (2 * 50)
a = (225 - 25) / 100
a = 200 / 100
a = 2 m/s²
So, the acceleration of the car is 2 m/s².
Now, let's calculate the time it took for the car to travel the given distance using the equation of motion:
s = ut + (1/2)at²
Rearranging the formula to solve for time:
t = √((2s) / a)
Substituting the given values:
t = √((2 * 50) / 2)
t = √(100 / 2)
t = √50
t ≈ 7.07 seconds
Therefore, the time it took for the car to travel a distance of 50 m is approximately 7.07 seconds.