a car travels around a horizontal circular track of radius 45m. if the car increases its speed at a constant rate of 1.2m/s starting from rest, determine the time needed for it to reach an acceleration of 1.4m/s. What is its speed at this instant?
speed increases at a rate of 1.2m/s/?
If the speed increases, the value (m/s) increases by 1.2m.s every how often?
acceleration is not measured as m/s.
It looks to me like you should have written the acceleration is 1.2m/s^2, and you want to find how long it takes the speed to get to 1.4m/s.
That would be 1.4/1.2 seconds.
Naturally, at that time, the speed is 1.4m/s.
If I got it wrong, clarify and repost.
To determine the time needed for the car to reach an acceleration of 1.4 m/s and its speed at this instant, we need to break down the problem into steps:
Step 1: Find the time needed to reach the desired acceleration.
To find the time required to reach an acceleration of 1.4 m/s, we can use the following formula:
acceleration = change in velocity / time
Given that the car starts from rest (initial velocity, v0 = 0) and increases its speed at a constant rate (acceleration, a = 1.2 m/s^2), we can rearrange the formula to solve for time (t):
1.4 m/s = (change in velocity) / t
Rearranging the equation, we get:
change in velocity = 1.4 m/s * t
Step 2: Find the speed of the car at this instant.
The speed of the car at any instant can be calculated using the formula:
speed = initial velocity + acceleration * time
In this case, the initial velocity (v0) is 0 m/s, and the acceleration (a) is 1.2 m/s^2. We can use the time (t) found in step 1 to calculate the speed at this instant:
speed = 0 m/s + 1.2 m/s^2 * t
Step 3: Substitute the value of "t" to get the final answer.
We don't have the exact value of time (t), so we need to find it using the first equation we derived in Step 1. By substituting the value of "1.4 m/s" for the change in velocity, we can solve for "t":
1.4 m/s = (1.4 m/s * t) / t
Since "t" appears on both sides of the equation, it cancels out:
1.4 m/s = 1.4 m/s
This equation shows that any value of "t" would satisfy it. So, the time needed for the car to reach an acceleration of 1.4 m/s is not uniquely defined.
However, we can still calculate the speed of the car at this instant using the equation from Step 2:
speed = 0 m/s + 1.2 m/s^2 * t
By substituting any value for "t", we can calculate the speed at that specific instant.