Figure 5 is a speed-time graph of an object. Given that the total distance travelled by the object is 7200m, calculate the acceleration in the first 40 seconds.

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Asked on May 6, 2026Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

Accepted Answer · 2026-05-06T05:46:22.955Z

Welcome back More — missed you this week. Here are the solutions to your questions. 18. Figure 5 is a speed-time graph of an object. Given that the total distance travelled by the object is 7200m, calculate the acceleration in the first 40 seconds. Step 1: Calculate the total distance travelled in terms of the maximum speed, V. The total distance travelled is the area under the speed-time graph. The graph forms a trapezium. The parallel sides of the trapezium are the time intervals where the speed is non-zero. Length of the first parallel side (top) = 100\, s - 40\, s = 60\, s. Length of the second parallel side (bottom) = 120\, s - 0\, s = 120\, s. The height of the trapezium is the maximum speed, V. The formula for the area of a trapezium is (1)/(2) (a+b)h. Distance = (1)/(2) (60\, s + 120\, s) V Distance = (1)/(2) (180\, s) V Distance = 90V Step 2: Use the given total distance to find the maximum speed, V. We are given that the total distance travelled is 7200\, m. 90V = 7200\, m V = (7200)/(90)\, m/s V = 80\, m/s Step 3: Calculate the acceleration in the first 40 seconds. Acceleration is the gradient of the speed-time graph. In the first 40 seconds, the object accelerates from rest (u = 0\, m/s) to a final speed of V = 80\, m/s over a time interval of t = 40\, s. The formula for acceleration is a = (v - u)/(t). a = 80\, m/s - 0\, m/s40\, s a = 80\, m/s40\, s a = 2\, m/s^2 The acceleration in the first 40 seconds is 2 m/s^2. 19. Make u the subject of the formula A = (1)/(2) m (v^2 - u^2) Step 1: Multiply both sides by 2 to eliminate the fraction. 2A = m (v^2 - u^2) Step 2: Divide both sides by m. (2A)/(m) = v^2 - u^2 Step 3: Rearrange the equation to isolate u^2. Add u^2 to both sides and subtract (2A)/(m) from both sides. u^2 = v^2 - (2A)/(m) Step 4: Take the square root of both sides to solve for u. u = ± sqrt(v^2 - (2A)/(m)) The subject of the formula is u = ± sqrt(v^2 - (2A)/(m)). Drop the next question 📸

Accepted Answer · 2026-05-06T05:46:22.955Z

Welcome back More — missed you this week. Here are the solutions to your questions. 18. Figure 5 is a speed-time graph of an object. Given that the total distance travelled by the object is 7200m, calculate the acceleration in the first 40 seconds. Step 1: Calculate the total distance travelled in terms of the maximum speed, V. The total distance travelled is the area under the speed-time graph. The graph forms a trapezium. The parallel sides of the trapezium are the time intervals where the speed is non-zero. Length of the first parallel side (top) = 100\, s - 40\, s = 60\, s. Length of the second parallel side (bottom) = 120\, s - 0\, s = 120\, s. The height of the trapezium is the maximum speed, V. The formula for the area of a trapezium is (1)/(2) (a+b)h. Distance = (1)/(2) (60\, s + 120\, s) V Distance = (1)/(2) (180\, s) V Distance = 90V Step 2: Use the given total distance to find the maximum speed, V. We are given that the total distance travelled is 7200\, m. 90V = 7200\, m V = (7200)/(90)\, m/s V = 80\, m/s Step 3: Calculate the acceleration in the first 40 seconds. Acceleration is the gradient of the speed-time graph. In the first 40 seconds, the object accelerates from rest (u = 0\, m/s) to a final speed of V = 80\, m/s over a time interval of t = 40\, s. The formula for acceleration is a = (v - u)/(t). a = 80\, m/s - 0\, m/s40\, s a = 80\, m/s40\, s a = 2\, m/s^2 The acceleration in the first 40 seconds is 2 m/s^2. 19. Make u the subject of the formula A = (1)/(2) m (v^2 - u^2) Step 1: Multiply both sides by 2 to eliminate the fraction. 2A = m (v^2 - u^2) Step 2: Divide both sides by m. (2A)/(m) = v^2 - u^2 Step 3: Rearrange the equation to isolate u^2. Add u^2 to both sides and subtract (2A)/(m) from both sides. u^2 = v^2 - (2A)/(m) Step 4: Take the square root of both sides to solve for u. u = ± sqrt(v^2 - (2A)/(m)) The subject of the formula is u = ± sqrt(v^2 - (2A)/(m)). Drop the next question 📸

Figure 5 is a speed-time graph of an object. Given that the total distance travelled by the object is 7200m, calculate the acceleration in the first 40 seconds.

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Figure 5 is a speed-time graph of an object. Given that the total distance travelled by the object is 7200m, calculate the acceleration in the first 40 seconds.

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