1. A sprinter finishes the race with a velocity of 8.9 m/s. the sprinter accelerated to a stop at a rate of -2.7 m/s2. how long did it take the sprinter to come to a stop?
2. A cycllist starts from rest & reaches a velocity of 18 m/s southwest in 3.8 seconds. what was the cyclists acceleration?
3. a UFO is flying at a velocity of 45 m/s (E). if 5.9 seconds later it's velocity was 35 m/s (W) what was its acceleration? what assumption did you make?
4. a motorcycle & rider start from rest and reach a velocity of 50 km/h (E) in 2.7 seconds. what was the acceleration of the motorcycle in m/s2?
My answers
1. I don't get how to do it
2. 4.73 m/s2 (SW)
3. -1.69 m/s2 EW
4. 19.2 m/s2
I'm not sure i did these correctly so please help
#1
Keep track of the units. We want time, which is (m/s) / (m/s^2)
SO, divide the change in velocity by the acceleration used:
-8.9 m/s divided by -2.7 m/s^2 = 3.30 s
#2 ok
#3
The velocity change by 80 m/s in the W direction. This change took 5.9 seconds, so assuming constant acceleration, we have
80/5.9 = 13.56 m/s W
#4 the acceleration is
50/2.7 km/hr/s = 18.518 km/hr/s
But 1 km/hr = 1000/3600 m/s = 0.2777 m/s
So, 18.518 km/hr/s = 5.14 m/s^2
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1. To find the time it took for the sprinter to come to a stop, we can use the formula:
Final velocity (v) = Initial velocity (u) + (Acceleration (a) × Time (t))
In this case, the initial velocity (u) is 8.9 m/s, the acceleration (a) is -2.7 m/s², and the final velocity (v) is 0 m/s (since the sprinter came to a stop). Let's rearrange the formula to solve for time:
0 m/s = 8.9 m/s + (-2.7 m/s² × t)
Now, we can subtract 8.9 m/s from both sides:
-8.9 m/s = -2.7 m/s² × t
Dividing both sides by -2.7 m/s²:
t = -8.9 m/s / -2.7 m/s² ≈ 3.30 seconds
Therefore, it took the sprinter approximately 3.30 seconds to come to a stop.
2. The acceleration of the cyclist can be calculated using the formula:
Acceleration (a) = (Final velocity (v) - Initial velocity (u)) / Time (t)
Here, the initial velocity (u) is 0 m/s because the cyclist starts from rest, the final velocity (v) is 18 m/s southwest, and the time (t) is 3.8 seconds.
To account for direction, we should consider southwest as a vector quantity, which means it has both magnitude and direction. Since the velocity is given as southwest, we can break it down into its components. The magnitude of the velocity is 18 m/s, and the direction is southwest, which is at an angle of 45 degrees.
Using trigonometry, we can find the southwest component of the velocity:
Southwest velocity = magnitude of velocity × cos(45) ≈ 18 m/s × cos(45) ≈ 12.73 m/s
Now, we can calculate the acceleration:
Acceleration (a) = (12.73 m/s - 0 m/s) / 3.8 s ≈ 3.35 m/s²
Therefore, the cyclist's acceleration is approximately 3.35 m/s² southwest.
3. To find the acceleration of the UFO, we can use the equation:
Acceleration (a) = (Final velocity (v) - Initial velocity (u)) / Time (t)
Here, the initial velocity (u) is 45 m/s (east), the final velocity (v) is 35 m/s (west), and the time (t) is 5.9 seconds.
The assumption made here is that the acceleration is constant throughout the time interval of 5.9 seconds.
Now, we can calculate the acceleration:
Acceleration (a) = (35 m/s - 45 m/s) / 5.9 s ≈ -1.69 m/s²
The negative sign indicates that the UFO has decelerated or slowed down during this time interval.
Therefore, the UFO's acceleration is approximately -1.69 m/s² west.
4. To find the acceleration of the motorcycle, we need to convert the given final velocity from km/h to m/s.
Given: Final velocity = 50 km/h (east), Time = 2.7 seconds
First, let's convert the final velocity to m/s:
50 km/h = (50 × 1000) m / (60 × 60) s ≈ 13.89 m/s (east)
Now, we can use the formula:
Acceleration (a) = (Final velocity (v) - Initial velocity (u)) / Time (t)
Here, the initial velocity (u) is 0 m/s since the motorcycle starts from rest, the final velocity (v) is 13.89 m/s (east), and the time (t) is 2.7 seconds.
Now, we can calculate the acceleration:
Acceleration (a) = (13.89 m/s - 0 m/s) / 2.7 s ≈ 5.15 m/s²
Therefore, the acceleration of the motorcycle is approximately 5.15 m/s² (east).