The total distance travel by the truck during the time interval of and with the uniform acceleration is \(\boxed{82.688{\text{ m}}}\) or \(\boxed{82.69{\text{ m}}}\) or \(\boxed{82.7{\text{ m}}}\).
Further explain:
We have to calculate the distance travel during time interval of \(3.2{\text{ s}}\).
Given:
Initial velocity of the truck is \(22{{{\text{ m}}} \mathord{\left/ {\vphantom {{{\text{ m}}} {\text{s}}}} \right. \kern-
ulldelimiterspace} {\text{s}}}\)
The constant rate of increase of velocity, which is also known as uniform acceleration of the truck is \(2.4{{{\text{ m}}} \mathord{\left/ {\vphantom {{{\text{ m}}} {{{\text{s}}^2}}}} \right. \kern-
ulldelimiterspace} {{{\text{s}}^2}}}\).
Time duration of the motion of the truck is \(3.2{\text{ s}}\).
Formula and concept used:
For calculating the distance traveled by the truck during the time interval of \(3.2{\text{ s}}\).
Use the kinematic equation of the motion with uniform acceleration as,
\(S = ut + \dfrac{1}{2}a{t^2}\) …… (1)
Here, \(S\) is the distance travelled by the truck.
\(u\) is the initial velocity of the truck.
\(a\) is the acceleration of the truck or constant rate of change of acceleration.
\(t\) is the time duration of the motion of the truck with uniform acceleration.
Calculation:
Substitute the value of \(u\) as \(22{\text{ }}{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-
ulldelimiterspace} {\text{s}}}\) , value of \(a\) as \(3.2{\text{ }}{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {{{\text{s}}^2}}}} \right. \kern-
ulldelimiterspace} {{{\text{s}}^2}}}\) and the value of \(t\) as \(3.2{\text{ s}}\) in the equation (1).
\(\begin{gathered}S=22 \times 3.2 + \frac{1}{2} \times 2.4 \times {3.2^2} \hfill\\S=70.4 + 12.288\hfill\\S=82.688{\text{ m}} \hfill\\S\approx 82.7{\text{ m}}\hfill\\\end{gathered}\)
So, the truck will travel the distance of \(82.7{\text{ m}}\) during the time interval of \(3.2{\text{ s}}\) with the uniform acceleration of \(2.4{\text{ }}{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {{{\text{s}}^2}}}} \right. \kern-
ulldelimiterspace} {{{\text{s}}^2}}}\).
Learn more:
- Motion under friction https://brainly.com/question/7031524.
2. Conservation of momentum https://brainly.com/question/9484203.
3. Expansion of gases https://brainly.com/question/9979757.
Answer details:
Grade: Senior school
Subject: Physics
Chapter: Kinematics
Keywords:
A truck, speed, 22m/s, increase, speed, constant rate, total distance traveled, time interval, acceleration, decelerate, velocity, time, change.
