A car with an initial speed of 23.7 km/h accelerates at a uniform rate of 0.92 m/s^2 for 3.6s. Find the final speed and the displacement of the car during this time.
To find the final speed of the car, we can use the equation:
Final speed = Initial speed + (Acceleration x Time)
Given:
Initial speed (u) = 23.7 km/h
Acceleration (a) = 0.92 m/s^2
Time (t) = 3.6 s
Step 1: Convert the initial speed from km/h to m/s.
Initial speed in m/s = (23.7 km/h) * (1000 m / 1 km) * (1 h / 3600 s) = 6.5833 m/s (rounded to 4 decimal places)
Step 2: Calculate the final speed.
Final speed = 6.5833 m/s + (0.92 m/s^2 x 3.6 s) = 6.5833 m/s + 3.312 m/s = 9.8953 m/s (rounded to 4 decimal places)
Therefore, the final speed of the car is 9.8953 m/s.
To find the displacement of the car, we can use the equation:
Displacement = Initial velocity x Time + (1/2) x Acceleration x Time^2
Step 3: Calculate the displacement.
Displacement = (6.5833 m/s x 3.6 s) + (0.5 x 0.92 m/s^2 x (3.6 s)^2)
Displacement = 23.8 m + (0.5 x 0.92 m/s^2 x 12.96 s^2)
Displacement ≈ 23.8 m + 6.0038 m
Displacement ≈ 29.804 m (rounded to 4 decimal places)
Therefore, the displacement of the car during this time is approximately 29.804 meters.
To find the final speed of the car, we can use the formula:
Final speed = Initial speed + (Acceleration x Time)
Given:
Initial speed (Vi) = 23.7 km/h
Acceleration (a) = 0.92 m/s^2
Time (t) = 3.6 s
We need to convert the initial speed from km/h to m/s.
Step 1: Convert the initial speed from km/h to m/s.
1 km/h = 1000 m / 3600 s = 0.2778 m/s
Initial speed (Vi) = 23.7 km/h x 0.2778 m/s = 6.58 m/s (rounded to two decimal places)
Now we can calculate the final speed:
Final speed = 6.58 m/s + (0.92 m/s^2 x 3.6 s)
Final speed = 6.58 m/s + 3.312 m/s = 9.892 m/s (rounded to three decimal places).
Therefore, the final speed of the car is 9.892 m/s.
Now let's find the displacement of the car during this time. We can use the formula:
Displacement = (Initial speed x Time) + (0.5 x Acceleration x Time^2)
Displacement = (23.7 km/h x 0.2778 m/s) x 3.6 s + (0.5 x 0.92 m/s^2 x (3.6 s)^2)
Displacement = 6.58 m/s x 3.6 s + 0.5 x 0.92 m/s^2 x 12.96 s^2
Displacement = 23.688 m + 7.1232 m
Displacement = 30.8112 m (rounded to four decimal places)
Therefore, the displacement of the car during this time is 30.8112 m.
Final speed = Vi + a(t)
Displacement = Vi(t) + 1/2a(t)^2
Final Velocity= VI + a(t)
Distance= 1/2 (VI + VF)(t)
you must first convert km/h to m/s and then you should be able to find your answers