Question #7003

a taxi driver allows his taxi cab weighing 17.08 kN to coast in neutral, and air resistance decelerates the car from 35.8 m/s to 22.4 m/s in a period of 24 seconds. calculate (a) the average deceleration, (b) the displacement of the car while it is decelerating.

Expert's answer

(a) the average deceleration

Let a be the average deceleration. Then

V(t) = at + V0.

We know that

V(T) = V1, so

aT + V0 = V1, or

24a + 35.8 = 22.4 ==> a = (22.4-35.8)/24 = -67/120 m/s².

(b) the displacement of the car while it is decelerating.

We'll use the formula

D(t) = at²/2 + V0*t.

So,

D(T) = aT²/2 + V0*T = -67/120*24²/2 + 35.8*24 = 3492/5 m.

Let a be the average deceleration. Then

V(t) = at + V0.

We know that

V(T) = V1, so

aT + V0 = V1, or

24a + 35.8 = 22.4 ==> a = (22.4-35.8)/24 = -67/120 m/s².

(b) the displacement of the car while it is decelerating.

We'll use the formula

D(t) = at²/2 + V0*t.

So,

D(T) = aT²/2 + V0*T = -67/120*24²/2 + 35.8*24 = 3492/5 m.

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