Speed, Average Acceleration, and Velocity

[slu1986]

1. At t = 0, an automobile traveling north begins to make a turn. It follows one-quarter of the arc of a circle of radius 9.3 m until, at t = 1.60 s, it is traveling east. The car does not alter its speed during the turn.
(a) Find the car's speed.
(b) Find the change in its velocity during the turn.
(c) Find its average acceleration during the turn.

Homework Equations

average speed = distance traveled/time of trip
change in velocity = vf - vi
average acceleration = Δv/Δt


3. I understand how to calculate the change in velocity and average speed and acceleration, however the problem throws me off b/c of the way it's set up..I am confused at where to begin solving this problem b/c of the radius and the whole arc thing. If someone could please help me get started I would appreciate it. Thanks.

 

[rl.bhat]

In the problem it is said that the car does not change its speed during the turn.
So during turn speed is constant.
The car is moving in a uniform circular motion. So the velocity is always tangential to the circular path. The velocity is a vector. It changes its direction from north to east. Let V1 in the north direction and V2 is in east direction.Their directions are perpendicular to each other. So the change in the velocity is V2 - V1. Their magnitudes are equal. To find the resultant of these vectors, along with V2 draw a vector in the south direction, And then find the resultant.
For the part c, what is the acceleration of the body which is moving in a uniform circular motion?

 

[tomcue]

Hello,

I can definitely help you get started with this problem. Let's break it down step by step.

First, we need to understand what the problem is asking for. We are given information about an automobile traveling north and then making a turn to the east. We are asked to find its speed, change in velocity, and average acceleration during this turn.

To start, we need to understand the concepts of speed, average acceleration, and velocity. Speed is the rate at which an object moves, calculated by dividing the distance traveled by the time it took to travel that distance. In this case, we are given the distance (quarter of a circle with a radius of 9.3 m) and the time (1.60 s), so we can use the formula for average speed to find the car's speed.

Average acceleration, on the other hand, is the rate at which an object's velocity changes over a period of time. In this problem, we are given the initial and final velocities, so we can use the formula for change in velocity to find the car's change in velocity during the turn.

Now, let's look at the car's path during the turn. It follows one-quarter of a circle with a radius of 9.3 m. This means that the car moves along an arc that is one-quarter of a circle with a radius of 9.3 m. To calculate the distance traveled, we can use the formula for arc length, which is s = rθ, where s is the distance traveled, r is the radius, and θ is the angle in radians. In this case, the angle θ is π/2 radians (one-quarter of a circle). So, the distance traveled by the car is s = (9.3 m)(π/2) = 4.65π m.

Now that we have the distance traveled, we can use the formula for average speed to find the car's speed. We know that the time it took to travel this distance is 1.60 s, so we can plug these values into the formula and solve for the speed:

average speed = distance traveled/time of trip
speed = (4.65π m)/(1.60 s) = 2.91 m/s

Next, we can use the formula for change in velocity to find the car's change in velocity during the turn. We know that the initial velocity is north and the final velocity is east