A car traveling 77 km/h slows down at a constant 0.50 m/s2 just by \"letting up

Question

A car traveling 77 km/h slows down at a constant 0.50 m/s2 just by "letting up on the gas."

Part A

Calculate the distance the car coasts before it stops.

Express your answer to two significant figures and include the appropriate units.

Part B

Calculate the time it takes to stop.

Express your answer to two significant figures and include the appropriate units.

Part C

Calculate the distance it travels during the first second.

Express your answer to two significant figures and include the appropriate units.

Part D

Calculate the distance it travels during the fifth second.

Express your answer to two significant figures and include the appropriate units.

Please show all work

Explanation / Answer

here,

initial speed of car , vi = 77 km/h = 21.39 m/s

accelration , a = - 0.5 m/s^2

(a)

let the distnace travelled be d

v^2 - vi^2 = 2*a* d

- 21.39^2 = - 2 * 0.5 * d

d = 457.48 m

the distance travelled is 457.48 m

(b)

let the time taken be t

v = vi + a * t

0 = 21.39 - 0.5 * t

t = 42.78 s

(c)

distance travelled during the first seccond

d' = vi*t - 0.5 * a*t^2

for t = 1 ,

d' = 21.39 - 0.5 * 0.5 * 1

d' = 21.14 m

(d)

speed after four seccond,

v4 = 21.39 - 0.5 * 4

v4 = 19.39 m/s

the distance travelled in fifth seccond

d5 = v4 * t - 0.5 * a * t^2

d5 = 19.39 - 0.5 * 0.5

d5 = 19.14 m

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