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Bumek
20 days ago
8

A car driving on a straight track accelerates at a rate of 3.2 m/s2 for 14 s. If the initial velocity of the car was 5.1 m/s, an

d its initial position was 0 m, what is its final position?
Mathematics
1 answer:
tester [8.8K]20 days ago
6 0

Result:

The information at hand includes:

The acceleration stands at 3.2 m/s² for a duration of 14 seconds.

Initial velocity is 5.1 m/s.

Starting position is 0m.

Therefore:

A(t) = 3.2m/s²

To derive the velocity, integration over time is performed where the constant of integration equals the initial velocity.

V(t) = (3.2m/s²)*t + 5.1 m/s

For the position equation, we integrate again over time, with the integration constant being the initial position (which is zero).

P(t) = (1/2)*(3.2 m/s²)*t² + 5.1m/s*t

The final position corresponds to when the car ceases to accelerate, occurring at t = 14s.

P(14s) =   (1/2)*(3.2 m/s²)*(14s)² + 5.1m/s*14s = 385m

Thus, the final position is 385 meters from the starting point.

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