a car moving with constant acceleration covers a distance between two points 180m apart in 6 sec.its speed as it passes the second point in 45m/s. what is its acceleration and its speed at the first point?
options:
1. -5 m/s^2;15m/s
2. 5 m/s^2;15m/s
To find the acceleration of the car, we can use the formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the car is moving with constant acceleration, let's assume the initial velocity at the first point is "u" m/s, and the acceleration is "a" m/s^2. The time taken to cover the distance between the two points is given as 6 seconds.
Using the equation for distance, we can write:
180 = (u * 6) + (0.5 * a * 6^2)
Simplifying this equation, we get:
180 = 6u + 18a
Next, we are given the speed of the car at the second point, which is 45 m/s. The speed can be calculated using the formula:
speed = initial velocity + (acceleration * time)
Using this formula, we can find the initial velocity at the second point:
45 = u + (a * 6)
Now we have two equations:
180 = 6u + 18a
45 = u + (a * 6)
We can solve these equations simultaneously to find the values of "a" and "u".
Solving the first equation, we can rearrange it as:
6u = 180 - 18a
u = (180 - 18a)/6
u = 30 - 3a
Now, let's substitute the value of "u" from this equation into the second equation:
45 = (30 - 3a) + (a * 6)
45 = 30 - 3a + 6a
45 - 30 = 3a
15 = 3a
a = 15/3
a = 5 m/s^2
Therefore, the acceleration of the car is 5 m/s^2.
To find the speed at the first point, we can substitute the value of "a" into the equation for "u":
u = 30 - 3a
u = 30 - 3 * 5
u = 30 - 15
u = 15 m/s
Therefore, the speed of the car at the first point is 15 m/s.
So, the correct answer is option 2: 5 m/s^2; 15 m/s.