Answer:
1) an expression for the car's speed is given as
v = u + at
where
v is the car's speed
u is the initial speed of the car
a is the car's acceleration
t is the time spent accelerating
2) The car does not hit the tree limb
Explanation:
The initial velocity of the car = 0 m/s (since it accelerates from rest)
acceleration of the car = 1.76 m/s
time spent accelerating = 20 s
For the car's speed just before the driver begins braking, we use the expression
v = u + at
where v is the final speed of the car just before the driver begins braking
u is the initial velocity with which the car starts moving
a is the acceleration of the car
t is the time spent accelerating from u to v
substituting values, we have
v = 0 + 1.76(20)
v = 0 + 35.2
the car's speed v = 35.2 m/s
In this time the car accelerates, the car moves a distance given by
s = ut + [tex]\frac{1}{2}[/tex]a[tex]t^2[/tex]
where s is the distance covered in this time
u is the initial speed of the vehicle
a is the acceleration
t is the time taken
substituting, we have
s = 0(20) + [tex]\frac{1}{2}[/tex](1.76)[tex]20^{2}[/tex]
s = 0 + 352
distance s = 352 m
When the driver brakes, we have
time spent braking = 5 s
acceleration = -5.93 m/s
and the distance to the limb = 550 m from where the car begun
to get the distance covered in this period, we use the expression
s = ut + [tex]\frac{1}{2}[/tex]a[tex]t^2[/tex]
where s is the distance traveled at this time
u is the speed of the car before it starts braking = 35.2 m/s
a is the acceleration at this point
t is the time taken to decelerate to a stop
substituting values, we have
s = 35.2(5) + [tex]\frac{1}{2}[/tex](-5.93 x [tex]5^2[/tex])
s = 176 - 74.125
s = 101.88 m
Total distance moved by the car = 352 m + 101.88 m = 453.88 m
Since the total distance traveled by the car is less than the distance from the starting point to the place where the tree limb is, the car does not hit the tree limb.
