A car accelerates in the +x direction from rest with a constant acceleration of

Question

A car accelerates in the +x direction from rest with a constant acceleration of a1 = 1.8 m/s2 for t1 = 20 s. At that point the driver notices a tree limb that has fallen on the road and brakes hard with a constant acceleration of a2 = -8.52 m/s2. A) Enter an expression, in terms of defined quantities, for the car's speed just before the driver begins braking, v1. B) If the limb is on the road at a distance of 550 meters from where the car begins its initial acceleration, will the car hit the limb?

Explanation / Answer

A) just before breaking,

v = vo + a*t

= 0 + a1*t1

= a1*t1

B) v = 1.8*20

= 36 m/s

let d1 is the distance travelled during 1st 20s,

use, d1 = u*t1 + (1/2)*a1*t1^2

= 0 + (1/2)*1.8*20^2

= 360 m

let d2 is the distance travelled before coming to rest.

use, vf^2 - vi^2 = 2*a*d2

==> d2 = (vf^2 -vi^2)/(2*a)

= (0^2 - 36^2)/(2*(-8.52))

= 76 m

total distance travelled, d = d1 + d2

= 360 + 76

= 436 m < 550 m

so, car cant hit the limb.

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