A car starts from rest on a curve with a radius of 150m and tangential acceleration of 1.5m/s2 .
Through what angle will the car have traveled when the magnitude of its total acceleration is 2.6m/s2 ?
To find the angle traveled by the car, we need to use the concept of centripetal acceleration and tangential acceleration.
First, let's find the centripetal acceleration (ac) using the radius (r) and the tangential acceleration (at):
ac = (v^2) / r
Since the car starts from rest, its initial velocity is 0. The tangential acceleration (at) is given as 1.5 m/s^2. Therefore, the centripetal acceleration can be calculated as:
ac = (0^2) / 150
ac = 0
Next, let's calculate the total acceleration (a) using the centripetal acceleration (ac) and the tangential acceleration (at):
a^2 = ac^2 + at^2
(2.6)^2 = 0 + (1.5)^2
6.76 = 2.25
a ≈ √6.76
a ≈ 2.6 m/s^2
Now, we want to find the angle (θ) the car has traveled when the total acceleration is 2.6 m/s^2. To find θ, we can use the formula:
a = r * θ
Rearranging the formula, we have:
θ = a / r
Plugging in the values, we get:
θ = 2.6 / 150
θ ≈ 0.017 rad
Therefore, the car will have traveled approximately 0.017 radians when the magnitude of its total acceleration is 2.6 m/s^2.