A car starts from rest and travels for 5s with a uniform acceleration of 1.5m/s^2. The driver then applies the break, causing a uniform acceleration of -2m/s^2, If the breaks are applied for 3s a) how fast is the car going at the end of the breaking period and b) how far has the car gone?
The initial speed of the car is
The acceleration for the first 5 s is
The displacement of the car in the first five seconds is
And the velocity of the car at 5 s is
Now for the next 3 s, the acceleration of the car is
So, the displacement covered in next 3 s is
So, the total distance traveled by the car from the beginning is
And the velocity of the car after this 3 s is
So, the speed of the car at the end of the breaking period is 1.5 m/s.
And the car has gone a distance of 32.25 m.
To solve this problem, we can break it down into two parts: the initial acceleration phase and the braking phase.
a) Initial acceleration phase: Given: Initial velocity (u) = 0 m/s (car starts from rest) Acceleration (a) = 1.5 m/s^2 Time (t) = 5 s
Using the equation of motion: v = u + at, where v is the final velocity, we can calculate the velocity at the end of the initial acceleration phase:
v = u + at v = 0 + (1.5)(5) v = 7.5 m/s
Therefore, at the end of the initial acceleration phase, the car's velocity is 7.5 m/s.
b) Braking phase: Given: Acceleration (a) = -2 m/s^2 (negative because it opposes the car's motion) Time (t) = 3 s
Using the same equation of motion, we can calculate the distance traveled during the braking phase:
s = ut + (1/2)at^2, where s is the distance traveled
Since the initial velocity for the braking phase is the final velocity from the initial acceleration phase (v = 7.5 m/s), we have:
s = (7.5)(3) + (1/2)(-2)(3)^2 s = 22.5 - 9 s = 13.5 m
Therefore, during the braking phase, the car travels a distance of 13.5 meters.
To summarize: a) At the end of the braking period, the car's speed is 7.5 m/s. b) The car has traveled a distance of 13.5 meters.
A car starts from rest and travels for 5s with a uniform acceleration of 1.5m/s^2. The...
A car starts from rest and travels for 10.0 s with a uniform acceleration of +1.8 m/s2. The driver then applies the brakes, causing a uniform acceleration of -2.5 m/s2. If the brakes are applied for 2.0 s, determine each of the following. (a) How fast is the car going at the end of the braking period? m/s (b) How far has the car gone? Om Need Help? Read It
A car starts from rest and travels for6.0 s with a uniform acceleration of+1.6m/s2. The driver then applies the brakes, causing auniform acceleration of-1.0 m/s2. If the brakes are applied for2.0 s, determine each of thefollowing.(a) How fast is the car going at the end of thebraking period?1 m/s(b) How far has it gone?2 m
1. A car starts from rest and travels for 8.0 s with a uniform acceleration of +1.8 m/s2. The driver then applies the brakes, causing a uniform acceleration of −1.5 m/s2. If the brakes are applied for 2.0 s, determine each of the following. (a) How fast is the car going at the end of the braking period? (m/s) (b) How far has the car gone? (m) 2. A ball is hit with a paddle, causing it to travel straight...
A truck covers 40.0 m in 9.45 s while uniformly slowing down to a final velocity of 2.35 m/s. (a) Find the truck's original speed. ________m/s (b) Find its acceleration. _________ m/s2 A car starts from rest and travels for 7.5 s with a uniform acceleration of +3.0 m/s2. The driver then applies the brakes, causing a uniform acceleration of −1.5 m/s2. If the brakes are applied for 2.0 s, determine each of the following. (c) How fast is the...
A car accelerates from rest with a constant acceleration of 1.5m/s^2 for 14 seconds . the car then continues traveling at the constant velocity with the speed it achieved after the 14 seconds of acceleration . it travels at this constant velocity for an additional 25 seconds. how far did the car travel during this whole motion?
Starting from rest, a truck travels in a straight line for 8.0 s with a uniform acceleration of +2.0 m/s2. The driver then applies the brakes for 2.0 s, causing a uniform acceleration of −3.0 m/s2 over that time. (a) What is the truck's speed at the end of the braking period? m/s (b) What is the total distance traveled by the truck (from the point where it started at rest to the end of the braking period)? m
Car A and B start a race from rest. Car A starts with an acceleration of 100 m/s^2 and after 10s increases with acceleration to 200 m/s^2. Car B starts with an acceleration of 50 m/s^2 and after 5s increases the acceleration to 300 m/s^2. 1) What is the distance between cars after 1s 2) What is the velocity of each car after 1s 3) After 30 seconds which car is ahead?
(20 points) A car starting from rest travels 220 m in 9.4 seconds with a constant acceleration. It then travels at a constant speed for another 12 seconds. After that, the brakes are applied and the car comes to rest an acceleration of 6.5 m/s2. A) Draw the motion diagram for the entire trip. B) What direction is the acceleration when the car is coming to rest? C) List all known variables with their values. D) What is the acceleration...
30). In the first 3s after a car starts from rest with an acceleration of 4 m/s 2 it will travel... A. 6 m B. 12 m C 18 m D. 72 m
The tangential acceleration of a car that starts from rest at A is (90 + s)/ 450 m/s^2, where s is the distance in meters measured along the curse from A. Compute the acceleration vector of the car when it is at B.