A car starts from rest and travels for 4.9 s with a uniform acceleration of +1.8 m/s2. The driver then applies the brakes, causing a uniform acceleration of -1.7 m/s2. The breaks are applied for 1.50 s.
1) How fast is the car going at the end of the breaking period?
2) How far has the car gone from its start?
Lets look at momentum.
The impulse equation ought to equal the final momentum.
F1*time1+F2*time2=mass*vfinal
but Force= mass*acceleration.
mass*1.8*4.9-mass*1.7*1.5= mass*Vfinal
solve for Vfinal.
How far?
distance= avg velocity*time
= Vf/2 * (1.5+4.9)
To find the answers to these questions, we can use the equations of motion. Let's break down the problem into two parts: the initial acceleration phase and the braking phase.
1) How fast is the car going at the end of the braking period?
During the initial acceleration phase, we can use the equation:
v = u + at
where:
v is the final velocity,
u is the initial velocity (which is zero since the car starts from rest),
a is the uniform acceleration, and
t is the time period.
Given: a = +1.8 m/s^2 and t = 4.9 s
Plugging in these values into the equation, we get:
v = 0 + (1.8 m/s^2)(4.9 s)
v = 8.82 m/s
Therefore, the car is going at a speed of 8.82 m/s at the end of the acceleration phase.
During the braking phase, we can use the same equation, but with the acceleration being negative since the car is decelerating:
v = u + at
Given: a = -1.7 m/s^2 and t = 1.50 s
Plugging in these values, we get:
v = 0 + (-1.7 m/s^2)(1.50 s)
v = -2.55 m/s
Therefore, the car is going at a speed of -2.55 m/s at the end of the braking phase.
2) How far has the car gone from its start?
To find the distance traveled by the car, we can use the equation of motion:
s = ut + 0.5at^2
where:
s is the distance traveled,
u is the initial velocity,
t is the time period, and
a is the uniform acceleration.
During the initial acceleration phase, we can use this equation with u = 0:
s1 = (0)(4.9 s) + 0.5(1.8 m/s^2)(4.9 s)^2
s1 = 8.82 m
Therefore, the car has traveled a distance of 8.82 meters during the acceleration phase.
During the braking phase, we can use the same equation, but with the velocity being the negative value since the car is decelerating:
s2 = (0)(1.50 s) + 0.5(-1.7 m/s^2)(1.50 s)^2
s2 = -1.91325 m
Therefore, the car has traveled a distance of -1.91325 meters during the braking phase.
To find the total distance traveled by the car, we can add the distances from both phases:
Total distance = s1 + s2 = 8.82 m - 1.91325 m
Total distance = 6.90675 m
Therefore, the car has traveled a total distance of approximately 6.90675 meters from its start.