Velocity and displacement with uniform acceleration:
1. A car with an initial speed of 23.7 km/h accelerates at a uniform rate of 0.92 m/s^2 for 3.6 s. Find the final speed and the displacement of the car during this time.
The final speed is 36 km/h. is this right? did i do the significant figures right?
Displacement: .030 km
2. A driver of a car traveling at 15.0 m/s applies the brakes, causing a uniform acceleration of -2.0 m/s^2. How long does it take the car to accelerate to a final speed of 10.0 m/s? How far has the car moved during the braking period?
2.5 s to accelerate to final speed
31.25 m - displacement
Your answers look alright to me. For 2. there are only 2 sig figs since accel is-2.0, so I think the final answer is 31m. The sig figs looked ok for 1.
For both questions, it seems like you have calculated the final speed and displacement correctly. However, I'll go through the step-by-step process of how to calculate them just to make sure.
1. First, let's convert the initial speed from km/h to m/s:
Initial speed = 23.7 km/h = 23.7 * (1000/3600) m/s ≈ 6.583 m/s (rounded to four significant figures)
2. To find the final speed, use the equation:
Final speed = Initial speed + (acceleration * time)
Final speed = 6.583 m/s + (0.92 m/s^2 * 3.6 s) ≈ 10.7492 m/s (rounded to four significant figures)
Converting this back to km/h:
Final speed = 10.7492 m/s * (3600/1000) km/h ≈ 38.697 km/h (rounded to four significant figures)
So, the final speed is approximately 38.7 km/h.
3. To calculate the displacement, use the following formula:
Displacement = Initial speed * time + (1/2 * acceleration * time^2)
Displacement = 6.583 m/s * 3.6 s + (1/2 * 0.92 m/s^2 * (3.6 s)^2) ≈ 22.29744 m (rounded to five significant figures)
Converting this back to kilometers:
Displacement = 22.29744 m * (1/1000) km/m ≈ 0.0223 km (rounded to four significant figures)
So, the displacement is approximately 0.0223 km.
For the second question:
1. The initial speed is given as 15.0 m/s, and the final speed is 10.0 m/s.
2. The acceleration is given as -2.0 m/s^2 (negative because the car is braking).
To find the time taken to accelerate, you can use the equation:
Final speed = Initial speed + (acceleration * time)
Rearranging this equation, we get:
Time = (Final speed - Initial speed) / acceleration
Time = (10.0 m/s - 15.0 m/s) / -2.0 m/s^2 = 2.5 s
So, the car takes 2.5 seconds to accelerate to a final speed of 10.0 m/s.
To calculate the displacement, you can use the formula:
Displacement = (Initial speed * time) + (1/2 * acceleration * time^2)
Displacement = (15.0 m/s * 2.5 s) + (1/2 * -2.0 m/s^2 * (2.5 s)^2) = -31.25 m
The negative sign indicates that the car has moved in the opposite direction of the initial motion.
So, the car has moved a distance of 31.25 meters during the braking period.