The value of the acceleration is 0.76 m/s² and the total time taken by the vehicle is 39 seconds.
<h3>Acceleration of the vehicle</h3>
The acceleration of the vehicle before coming to rest is calculated as follows;
v² = u² + 2as
where;
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- s is the distance traveled before stopping
the car came to rest with constant velocity attained after 12 seconds.
the initial velocity of the car before 12 seconds is zero.
v² = 0 + 2as
a = v²/2s
a = (10²)/(2 x 66)
a = 0.76 m/s²
<h3>Time of motion of the vehicle</h3>
d = ut + ¹/₂at²
where;
- d is the total distance traveled
- t is the time of motion
- a is acceleration
- u is initial velocity of the vehicle
580 = 0 + ¹/₂(0.76)t²
580 = 0.38t²
t² = 580/0.38
t² = 1,526.3
t = √1,526.3
t = 39 seconds
Thus, the value of the acceleration is 0.76 m/s² and the total time taken by the vehicle is 39 seconds.
Learn more about time of motion here: brainly.com/question/2364404
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