A lorry of mass 1000kg moving initially at 10m/s increases to 25m/s. In 5sec the on the lorry is 15,000Newtons; calculate:
(a) Acceleration
(b) The distance covered
You left out some words here:
"in 5 sec the on the lorry is 15,000 Newtons. "
Is 5 seconds the time requred to accelerate from 10 to 25 m/s? If so, there are two ways to calculate acceleration, and they do not agree.
To calculate the acceleration, we can use the formula:
Acceleration (a) = (Change in velocity) / (Time taken)
The change in velocity can be calculated by subtracting the initial velocity from the final velocity:
Change in velocity = Final velocity - Initial velocity
(a) Acceleration:
Change in velocity = 25 m/s - 10 m/s = 15 m/s
Time taken = 5 sec
Acceleration (a) = (15 m/s) / (5 sec)
Acceleration (a) = 3 m/s^2
So, the acceleration of the lorry is 3 m/s^2.
To calculate the distance covered, we can use the formula:
Distance covered = Initial velocity × Time taken + 0.5 × Acceleration × (Time taken)^2
(b) Distance covered:
Initial velocity = 10 m/s
Time taken = 5 sec
Acceleration = 3 m/s^2
Distance covered = (10 m/s) × (5 sec) + 0.5 × (3 m/s^2) × (5 sec)^2
Distance covered = 50 m + 0.5 × 3 m/s^2 × 25 sec^2
Distance covered = 50 m + 0.5 × 3 m/s^2 × 625 sec^2
Distance covered = 50 m + 0.5 × 3 m/s^2 × 625 sec^2
Distance covered = 50 m + 0.5 × 3 m/s^2 × 625 sec^2
Distance covered = 50 m + 937.5 m
Distance covered = 987.5 m
So, the distance covered by the lorry is 987.5 meters.