A 3000 lb car has an initial velocity of 10 mi/h. How much force is required to accelerate the car to a speed of 50 mi/h in 10 seconds?
Good grief, English units, have to put mass in slugs and use seconds and pounds and feet. (Back to freshman year in 1955)
change in speed = 40 miles/ hr *5280 feet/mile * 1 hr/3600 seconds
= 58.7 feet per second
mass in slugs = 3000 lb /32 ft/s^2
= 93.8 slugs
F = change in momentum/ time
F = 93.8 * 58.7 / 10 = 550 pounds
To find the force required to accelerate the car, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a).
First, let's convert the car's mass from pounds to slugs. 1 slug is the mass that accelerates at 1 ft/s^2 under a force of 1 pound. Since the car weighs 3000 pounds, we can divide that by the acceleration due to gravity to get its mass in slugs. The acceleration due to gravity is approximately 32.2 ft/s^2. So, the car's mass is 3000 lb / 32.2 ft/s^2 = 93.17 slugs (rounded to two decimal places).
Next, let's convert the initial velocity from miles per hour (mi/h) to feet per second (ft/s). There are 5280 feet in a mile and 3600 seconds in an hour, so we can convert 10 mi/h to ft/s by multiplying it by 5280 ft/mi and dividing by 3600 s/h. The initial velocity is then 10 mi/h * 5280 ft/mi / 3600 s/h = 14.67 ft/s (rounded to two decimal places).
Similarly, we convert the final velocity of 50 mi/h to ft/s: 50 mi/h * 5280 ft/mi / 3600 s/h = 73.33 ft/s (rounded to two decimal places).
Now, we can find the acceleration (a) using the equation:
a = (v - u) / t
where a is acceleration, v is final velocity, u is initial velocity, and t is time. Plugging in the values:
a = (73.33 ft/s - 14.67 ft/s) / 10 s
a = 58.67 ft/s / 10 s
a = 5.87 ft/s^2 (rounded to two decimal places)
Finally, we can calculate the force (F) required to accelerate the car using the equation:
F = m * a
where F is force, m is mass, and a is acceleration. Plugging in the values:
F = 93.17 slugs * 5.87 ft/s^2
F = 546.56 lb (rounded to two decimal places)
Therefore, the force required to accelerate the car to a speed of 50 mi/h in 10 seconds is approximately 546.56 pounds.