Attempting to stop on a slippery road a car moving at 80km/h
skidsacross the road at a 30 degree angle to its initial motion
comingto a stop in 3.9s. Determine the average acceleration in
m/s^2,using a coordinate system with x axis in the direction of the
car'soriginal motion and the y axis toward the side of the road to
whichthe car skids.
skidsacross the road at a 30 degree angle to its initial motion
comingto a stop in 3.9s. Determine the average acceleration in
m/s^2,using a coordinate system with x axis in the direction of the
car'soriginal motion and the y axis toward the side of the road to
whichthe car skids.
Answer
Given that
The initial velocity of the car (u) =80km/h
=
22.22m/s
22.22m/s
The angle made across the road(θ) =300
The time taken for the car to stop (Δt) =3.9s
Diagram:
Now the horizontal component of velocity(vx)
=ucosθ
=ucosθ
=
(22.22m/s)cos300
(22.22m/s)cos300
=
19.24m/s
19.24m/s
Vertical component (vy) = usinθ
=
(22.22m/s)sin300
(22.22m/s)sin300
=
11.11m/s
11.11m/s
Now the final velocity (vf) =
√vx2+vy2
√vx2+vy2
=
22.21m/s
22.21m/s
This will be the initial velocity of the car
beforeskidding
beforeskidding
The final velocity of the car after stop (vf')
=0m/s
=0m/s
Then the average acceleration of the car is given by
aavg
= vf' -vf /Δt
= vf' -vf /Δt
=-22.21m/s/3.9s
=
-5.694m/s2
-5.694m/s2
