Question

Select one of the equations below to help you answer questions 18-20. $$ \text { time }=\text { distance } \div \text { speed } $$ or speed \(=\) distance \(\div\) time It recently was estimated that \(T\). rex could run no faster than about \(11 \mathrm{~m} / \mathrm{s}\). At this speed, how long would it take \(T\). rex to run \(200 \mathrm{~m}\) ?

Short answer

It would take about 18.18 seconds.

Step-by-step solution

Identify Known Values

First, identify the known values from the problem. The speed of the T. rex is given as \(11\, \text{m/s}\) and the distance is \(200\, \text{m}\).

Choose the Right Formula

In order to find the time, we need to use the formula: \( \text{time} = \text{distance} \div \text{speed} \).

Substitute Known Values

Substitute the known values into the formula. \[\text{time} = \frac{200\, \text{m}}{11\, \text{m/s}} \]

Calculate the Time

Perform the division to calculate the time. \[\text{time} \approx 18.18\, \text{s} \]

Key concepts

Speed and Velocity

Understanding the difference between speed and velocity is essential in physics. Speed is a scalar quantity, which means it only has magnitude. It tells you how fast something is moving without considering direction. For instance, a car traveling at 60 km/h could be going in any direction, and its speed would remain 60 km/h.
A vital point to remember is the unit of speed. In the context of our exercise with the T. rex, speed is measured in meters per second (m/s). Speed gives you a snapshot of how quickly an object covers a distance.
Velocity, on the other hand, is a vector quantity. This means it has both magnitude and direction. If the car from earlier is moving at 60 km/h eastward, that describes the car's velocity. It tells not just how fast, but also where it's headed. In problems where direction is important, always consider velocity instead of just speed.

Distance and Time

Distance and time are intimately connected when studying motion. Distance describes the total path traveled by an object, while time measures the duration of the motion.
In our T. rex example, the dinosaur's race involves a specific distance, 200 meters, and our task is to find how long it takes, or the time required to cover that distance at a given speed.
The relationship between these three elements is captured by simple formulas. Knowing two allows you to solve for the third:

• If you know distance and speed, you can find time: \( \text{time} = \frac{\text{distance}}{\text{speed}} \)
• If you know speed and time, you can find distance: \( \text{distance} = \text{speed} \times \text{time} \)
• If you know distance and time, you can find speed: \( \text{speed} = \frac{\text{distance}}{\text{time}} \)

These equations are foundational in kinematics, helping us understand motion in a straightforward way.

Kinematic Equations

Kinematic equations are tools that let us calculate different aspects of an object's motion with constant acceleration. They help in predicting future motion and understanding past movement.
Even though the T. rex example uses a simplified version with constant speed (no acceleration), more complex situations use kinematic equations to solve real-world problems.
In general, kinematic equations relate:

• Initial velocity (\( v_i \)
• Final velocity (\( v_f \)
• Acceleration (\( a \)
• Time (\( t \)
• Displacement (\( s \)

A classic kinematic equation is:\[ s = v_i \cdot t + \frac{1}{2} a \cdot t^2 \]This equation helps us find the distance travelled when the initial velocity, time, and acceleration are known. While this wasn't needed for the T. rex, recognizing when acceleration comes into play helps you choose the right tools for solving motion problems.