The makers of a certain automobile advertise that it will accelerate from 15 to 50 mi/hr in high in 13 sec. Compute (a) the acceleration in ft/ sec2, and (b) the distance the car travels in this time, assuming the acceleration to be constant.
V1 = 15mi/h * 5280Ft/mi * 1h/3600s = 22Ft/s.
V2 = 50/15 * 22 = 73.3 Ft/s.
a. a = (V2-V1)/t=(73.3-22)/13 = 3.95 Ft/s.
b. d = V1*t + 0.5*a*t^2.
t = 13 s.
Solve for d.
To compute the acceleration in ft/sec², we first need to convert the speed from mi/hr to ft/sec.
1 mile is equal to 5280 feet, and 1 hour is equal to 3600 seconds. So, 1 mi/hr is equal to (5280 ft / 3600 sec) = 1.4667 ft/sec.
(a) Acceleration in ft/sec²:
Since the acceleration is the change in velocity divided by the time, we can calculate it by:
Acceleration = (Final velocity - Initial velocity) / Time
Given:
Initial velocity (u) = 15 mi/hr = 15 * 1.4667 ft/sec = 22 ft/sec
Final velocity (v) = 50 mi/hr = 50 * 1.4667 ft/sec = 73.34 ft/sec
Time (t) = 13 sec
Acceleration = (73.34 ft/sec - 22 ft/sec) / 13 sec
Acceleration = 51.34 ft/sec / 13 sec
Acceleration = 3.95 ft/sec²
Therefore, the acceleration of the car is approximately 3.95 ft/sec².
(b) Distance traveled:
To find the distance traveled, we can use the formula:
Distance = Initial velocity * Time + 0.5 * Acceleration * Time²
Given:
Initial velocity (u) = 22 ft/sec
Time (t) = 13 sec
Acceleration (a) = 3.95 ft/sec²
Distance = 22 ft/sec * 13 sec + 0.5 * 3.95 ft/sec² * (13 sec)²
Distance = 286 ft + 0.5 * 3.95 ft/sec² * 169 sec²
Distance = 286 ft + 0.5 * 664.55 ft
Distance = 286 ft + 332.275 ft
Distance = 618.275 ft
Therefore, the car will travel approximately 618.275 ft in this time, assuming the acceleration to be constant.
To find the acceleration in ft/sec^2 and the distance the car travels, we will use the equations of motion.
(a) To find the acceleration in ft/sec^2, we need to convert the speed from miles per hour to feet per second.
1 mile = 5280 feet
1 hour = 3600 seconds
First, let's convert the initial and final speeds from miles per hour to feet per second:
Initial speed: 15 mi/hr = (15 * 5280) / 3600 ft/sec
Final speed: 50 mi/hr = (50 * 5280) / 3600 ft/sec
Now, we can calculate the acceleration using the equation:
Acceleration (a) = (Final speed - Initial speed) / Time
Acceleration = ([(50 * 5280) / 3600] - [(15 * 5280) / 3600]) / 13
Calculate this expression to find the acceleration in ft/sec^2.
(b) To find the distance the car travels, we can use the equation:
Distance = (Initial speed * Time) + (0.5 * Acceleration * Time^2)
Substitute the values of initial speed, acceleration, and time to calculate the distance traveled in this time.
Distance = ([(15 * 5280) / 3600] * 13) + (0.5 * Acceleration * 13^2)
Compute this expression to find the distance traveled in feet.
By following these steps, you can find both the acceleration in ft/sec^2 and the distance the car travels in this scenario.