a car traveling on a straight road at 20 meters per second accelerates to 26 meters per second in 12 seconds. what is the total distance traveled by the car? please help!
I know that there are formulas in physics for this type of question, but I am not a physics teacher , so I will use standard Calculus
a = (v2 - v1)/(time2 - time1) = (26-20)/(12-0) = 6/12 = 1/2
since a = 1/2
v = (1/2)t + c
when t = 0, v = 20
20 = c
so v = (1/2)t + 20
then
d = (1/4)t^2 + 20t + k
at t=0 , d = k
at t = 12 , d = (1/4)(144) + 20(12) + k= 276+k
distance covered in that 12 seconds = 276k - k = 276 m
drwls or bobpursley could do it much easier.
To find the total distance traveled by the car, you need to calculate the distance traveled during acceleration and the distance traveled at a constant speed.
First, let's calculate the distance traveled during acceleration using the formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Given:
Initial velocity (u) = 20 m/s
Final velocity (v) = 26 m/s
Time (t) = 12 seconds
Since the car accelerates, we need to find the acceleration (a) using the formula:
acceleration = (final velocity - initial velocity) / time
Substituting the given values:
acceleration = (26 m/s - 20 m/s) / 12 s
Now, let's calculate the acceleration:
acceleration = 6 m/s / 12 s = 0.5 m/s^2
Substituting the acceleration value into the distance formula:
distance = (20 m/s * 12 s) + (0.5 m/s^2 * 12 s^2)
Now, calculate the distance during acceleration:
distance = (240 m) + (0.5 * 0.5 * 144 m)
distance = 240 m + 36 m = 276 m
The distance traveled during acceleration is 276 meters.
Next, let's calculate the distance traveled at a constant speed. Since the car maintains a constant speed after acceleration, the distance can be calculated using the formula:
distance = speed * time
Since the final velocity is 26 m/s, the distance traveled at a constant speed is:
distance = 26 m/s * (12 s - 0 s) = 312 m
The distance traveled at a constant speed is 312 meters.
To find the total distance traveled by the car, add the distance traveled during acceleration and the distance traveled at a constant speed:
Total distance = 276 m + 312 m = 588 meters
Therefore, the total distance traveled by the car is 588 meters.