In basic kinematics, which of the following correctly gives the formula for distance travelled by an object moving at constant speed for a given time?

Introduction / Context:
One of the first relationships students learn in physics is the simple formula connecting distance, speed, and time. It is widely used in everyday problems involving travel, such as finding how far a vehicle goes in a certain time at a given speed. This question checks your understanding of the correct algebraic relationship among these quantities when speed is constant.

Given Data / Assumptions:

• The object moves with constant speed.
• We consider a time interval t for which speed does not change.
• We want the formula that expresses distance travelled in terms of speed and time.

Concept / Approach:
Speed is defined as the distance travelled per unit time. In symbols, this is: speed = distance / time Rearranging this equation to make distance the subject gives: distance = speed × time This relation holds when speed is constant over the time interval considered, which is the case in this simple kinematics situation.

Step-by-Step Solution:
Step 1: Start from the definition of speed: speed = distance / time. Step 2: Multiply both sides by time to solve for distance. Step 3: This gives distance = speed × time. Step 4: Compare this final expression with the options and select the matching one.

Verification / Alternative check:
Consider an example: if a car travels at a constant speed of 60 km/h for 2 hours, the distance travelled is 60 × 2 = 120 km. This matches everyday reasoning and confirms that multiplying speed and time gives distance. Using any of the other suggested formulas would produce incorrect results that do not match reality.

Why Other Options Are Wrong:

• Distance = time ÷ speed: This is a rearrangement that would make units inconsistent, giving time squared per length, which is not appropriate for distance.
• Distance = speed × acceleration: Multiplying speed and acceleration gives units of m^2/s^3 in SI units, which does not correspond to distance and has no standard physical meaning in this context.
• Distance = velocity ÷ speed: Velocity and speed have the same units, so their ratio is dimensionless and cannot represent distance, which must have units of length.

Common Pitfalls:
Students sometimes mix up the roles of variables and may incorrectly believe that distance is speed divided by time, which reverses the correct relationship. Dimensional analysis is a good tool to catch such mistakes: distance must have units of length, while speed has length per time and time has units of time, so multiplying speed by time gives length. Remembering and checking units will often prevent formula errors.

Final Answer:
The correct formula is distance = speed × time.