A bus moving in a straight line at a speed of 20 m / s begins to slow at a constant rate of 3.0

Step 1: First, we need to identify the given values. The initial velocity $u_{i}$ is $20 mathrm{

A bus moving in a straight line at a speed of 20 m / s...

A bus moving in a straight line at a speed of $20 \mathrm{~m} / \mathrm{s}$ begins to slow at a constant rate of $3.0 \mathrm{~m} / \mathrm{s}$ each second. Find how far it goes before stopping. Take the direction of motion to be the $+x$ -direction. For the trip under consideration, $u_{i}=20 \mathrm{~m} / \mathrm{s}, v_{f}=0 \mathrm{~m} / \mathrm{s}, a=-3.0 \mathrm{~m} / \mathrm{s}^{2}$. Notice that the bus is not speeding up in the positive motion direction. Instead, it is slowing in that direction and so its acceleration is negative (a deceleration). Use $$ v_{f x}^{2}=v_{i x}^{2}+2 a x \quad \text { and, hence, } \quad 0=(20 \mathrm{~m} / \mathrm{s})^{2}+2\left(-3.0 \mathrm{~m} / \mathrm{s}^{2}\right) x $$ to find $$ x=\frac{-(20 \mathrm{~m} / \mathrm{s})^{2}}{2\left(-3.0 \mathrm{~m} / \mathrm{s}^{2}\right)}=67 \mathrm{~m} $$

A bus moving in a straight line at a speed of $20 \mathrm{~m} / \mathrm{s}$ begins to slow at a constant rate of $3.0 \mathrm{~m} / \mathrm{s}$ each second. Find how far it goes before stopping.
Take the direction of motion to be the $+x$ -direction. For the trip under consideration, $u_{i}=20 \mathrm{~m} / \mathrm{s}, v_{f}=0 \mathrm{~m} / \mathrm{s}, a=-3.0 \mathrm{~m} / \mathrm{s}^{2}$. Notice
that the bus is not speeding up in the positive motion direction. Instead, it is slowing in that direction and so its acceleration is negative (a deceleration). Use
$$
v_{f x}^{2}=v_{i x}^{2}+2 a x \quad \text { and, hence, } \quad 0=(20 \mathrm{~m} / \mathrm{s})^{2}+2\left(-3.0 \mathrm{~m} / \mathrm{s}^{2}\right) x
$$
to find
$$
x=\frac{-(20 \mathrm{~m} / \mathrm{s})^{2}}{2\left(-3.0 \mathrm{~m} / \mathrm{s}^{2}\right)}=67 \mathrm{~m}
$$

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Key Concepts

Constant Acceleration

This concept involves situations where an object’s acceleration remains unchanged over time. In kinematics, assuming constant acceleration simplifies the problem because the motion can be described using a set of standard equations that relate displacement, velocity, acceleration, and time.

Kinematic Equations

Kinematic equations are a set of formulas used to describe the motion of objects under constant acceleration. One such equation, v² = u² + 2ax, directly relates initial velocity, final velocity, acceleration, and displacement, and is particularly useful for finding the distance traveled when the final velocity is known.

Sign Convention in Kinematics

Properly assigning signs to velocity and acceleration is crucial in physics. In problems involving deceleration, the acceleration is negative relative to the chosen positive direction. This careful consideration of sign ensures that the equations correctly represent the physical direction of motion and the opposing acceleration.

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