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You are driving your car eastward, and the traffic light ahead turns red. You apply the brakes for 3.00 s, and the velocity of the car decreases to +4.50 m/s. During this time, the car travels 26 m. What is the car's acceleration, including direction? (Hint: this is a two part problem. You need to find some other quantity before finding the displacement.)

Respuesta :

Answer:

a = - 2.77 m/s², westwards

Explanation:

Given:

Time, t = 3 seconds

Final velocity of the car, v = 4.50 m/s

Distance, s = 26 m

Now,

from Newton's equation of motion

v = u + at

where,

u is the initial speed of the car

a is the acceleration

on substituting the respective values, we get

4.5 = u + a × 3

or

u = 4.5 - 3a

also,

[tex]s=ut+\frac{1}{2}at^2[/tex]

on substituting the value, we get

[tex]26=(4.5-3a)\times3+\frac{1}{2}a\times9^2[/tex]

or

26 = 13.5 - 9a + 4.5a

or

- 4.5a = 12.5

or

a = - 2.77 m/s²

here, the negative sign depicts that the acceleration is in opposite direction to the motion of the car.

Thus, the direction of the car is opposite to the eastward i.e westwards

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