A car starting from rest accelerated uniformly to a velocity of 100kilometer per hour. A break is applied in 4seconds ,find it's acceleration and retardation
To find the acceleration and retardation of the car, we need to use the formulas for acceleration and deceleration.
Acceleration can be calculated using the formula:
Acceleration (a) = Change in velocity (Δv) / Time taken (Δt)
Given that the car starts from rest and accelerates uniformly to a velocity of 100 kilometers per hour (27.8 meters per second), we can calculate the acceleration.
Acceleration (a) = (Final velocity - Initial velocity) / Time taken
Final velocity = 100 km/hr = 27.8 m/s (converted from km/hr to m/s)
Initial velocity = 0 m/s (starting from rest)
Time taken = 4 seconds
Acceleration (a) = (27.8 m/s - 0 m/s) / 4 s
Acceleration (a) = 27.8 m/s / 4 s
Acceleration (a) = 6.95 m/s²
Therefore, the car's acceleration is 6.95 m/s².
Now, to find the retardation (deceleration), we need to calculate the change in velocity and use the same formula.
Change in velocity (Δv) = Final velocity - Initial velocity
Final velocity = 0 m/s (since the car comes to rest)
Initial velocity = 27.8 m/s (velocity before braking)
Change in velocity (Δv) = 0 m/s - 27.8 m/s
Change in velocity (Δv) = -27.8 m/s (negative sign indicates deceleration)
Retardation (r) = Change in velocity (Δv) / Time taken
Retardation (r) = -27.8 m/s / 4 s
Retardation (r) = -6.95 m/s²
Therefore, the car's retardation (deceleration) is -6.95 m/s². Note that the negative sign indicates deceleration or retardation.