a driver traveling 42 mph speeds up to 58 mph over distance of 660 feet how long does this increase in speed take what is the driver's acceleration
Well, now we seem to be back in the dark ages of some king's feet.
v1 = 42*5280/3600 ft/s
v2 = 58*5280/3600 ft/s
assuming constant acceleration we can use average v
va = 50*5280/3600 ft/s
so t = 660/va
a = (v2-v1)/t
To find the time it takes for the driver to increase speed and the driver's acceleration, we can use the equations of motion for constant acceleration. Here's how:
Step 1: Convert the speed from mph to feet per second (fps).
- 1 mph is approximately equal to 1.46667 feet per second.
- So, initial speed (v1) = 42 mph * 1.46667 fps/mph = 61.66694 fps
- Final speed (v2) = 58 mph * 1.46667 fps/mph = 85.13386 fps
Step 2: Calculate the change in velocity (Δv).
- Δv = v2 - v1 = 85.13386 fps - 61.66694 fps = 23.46692 fps
Step 3: Use the equation of motion v = u + at to find the time (t).
- Here, u is the initial speed, v is the final speed, and a is the acceleration.
- Rearrange the equation to solve for time: t = (v - u) / a
Step 4: Determine the acceleration.
- We can use the equation a = Δv / t rearranged as a = Δv / t
Now, let's calculate the time and acceleration.
Step 3 (continued): Calculate the time.
- t = (v2 - v1) / a
- t = 23.46692 fps / a
Step 4 (continued): Determine the acceleration.
- a = Δv / t
- Substituting the value of t obtained from Step 3:
- a = 23.46692 fps / ((23.46692 fps) / a)
- a = a
Step 5: Now we have the equation: t = 23.46692 / a.
To find the time and acceleration, we need another equation or piece of information.
Please provide additional information or constraints to solve for the time and acceleration.