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.

Answer 1

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.