a bus moving at 20m/s slows at a rate of 4m/s each second. how far does it travel while braking. i found the time which was 5 seconds.

Question

A car accelerates from rest at a rate of 5 m/s/s for a period of 4.2 seconds and then moves at a constant speed for 8 seconds more. how far did it travel.

a ball is launched at an angle of 30 degrees from the horizontal at a speed of 1.8 m/s/ what is the range? i found that vix=1.55 and viy=.90 then what do i do?

Answer 1

1. To find the distance traveled by the bus while braking, we can use the equation:

distance = initial velocity x time + 0.5 x acceleration x time^2

First, let's find the acceleration. Since the bus is slowing down, the acceleration is negative. The rate of slowing down is 4m/s each second, so the acceleration is -4 m/s².

Now, we can plug in the values into the equation:

distance = 20m/s x 5s + 0.5 x (-4 m/s²) x (5s)²

distance = 100m + (-0.5 x 4 m/s² x 25s²)

distance = 100m - 50m

distance = 50 meters

So, the bus travels 50 meters while braking.

2. To find the total distance traveled by the car, we need to find the distance traveled during acceleration and the distance traveled during constant speed separately.

First, let's find the distance traveled during acceleration:

distance = initial velocity x time + 0.5 x acceleration x time^2

Since the car starts from rest, the initial velocity is 0:

distance = 0.5 x 5 m/s² x (4.2s)²

distance = 0.5 x 5 m/s² x 17.64s²

distance = 44.1 meters

Now let's find the distance traveled at a constant speed. First, we need to find the final velocity of the car after acceleration using the formula:

final velocity = initial velocity + acceleration x time

final velocity = 0 + 5 m/s² x 4.2s

final velocity = 21 m/s

Now, we can find the distance traveled during constant speed:

distance = velocity x time

distance = 21 m/s x 8s

distance = 168 meters

So the total distance traveled is the sum of distances during acceleration and constant speed:

total distance = 44.1m + 168m

total distance = 212.1 meters

So, the car travels 212.1 meters in total.

3. To find the range, we first need to find the time of flight.

time of flight = 2 x (initial velocity y) / g

where g is the acceleration due to gravity, which is approximately 9.81 m/s².

time of flight = 2 x 0.90 m/s / 9.81 m/s²

time of flight ≈ 0.1837 seconds

Now, we can find the range using the horizontal velocity:

range = initial velocity x (time of flight)

range = 1.55 m/s x 0.1837s

range ≈ 0.2847 meters

So, the range of the ball is approximately 0.285 meters.