With a starting speed of 30 kph at point A, a car accelerates uniformly. After 18 minutes ,it reaches point B. 21 km from A. Find the acceleration of the car in m/s^2.
First, we need to convert the speed from km/h to m/s:
30 km/h * (1000 m/km) * (1h/3600s) = 8.33 m/s
Next, we need to convert the time from minutes to seconds:
18 minutes * 60s/1 minute = 1080 s
Now we can use the equation of motion:
v = u + at
where:
v = final velocity
u = initial velocity = 8.33 m/s
a = acceleration
t = time = 1080 s
Now, we need to find the final velocity:
v = u + at
v = 8.33 + a * 1080
Since the car accelerates uniformly, the final velocity is given by:
v^2 = u^2 + 2as
where:
v = final velocity
u = initial velocity = 8.33 m/s
a = acceleration
s = distance = 21 km = 21000 m
Now we can substitute v^2 into the equation:
(u + at)^2 = u^2 + 2as
(8.33 + a*1080)^2 = 8.33^2 + 2*a*21000
Expanding and simplifying this equation gives:
72a^2 + 8984a - 6743285 = 0
By solving this quadratic equation, we can find the value of acceleration (a) in m/s^2.